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THE 


ELEMENTS  OF  LOGIC, 


A    TEXT-BOOK 


FOR      SCHOOLS     AND      COLLEGES; 


THE    ELEMENTARY    LESSONS    IN    LOGIC. 

BY 

W.  STANLEY  JEVONS,  LL.D.,  F.R.S., 

LATE      PROFESSOR      OF      LOGIC      IN      OWENS     COLLEGE,      MANCHESTKK. 


RECAST     BY 
DAVID   J.   HILL,   LL.D:, 

:.mK8IDKNT  OP  THE   UKIVERSITT  OP  UOCHESTEB,   AND   AUTHOR  OP    HILL'& 
RHETORICAL   SERIES   AND  THE   ELEMENTS   OP  P3TCHOLOGY. 


NEW    YORK  • .  •  CINCINNATI  • .  •  CHICAGO 

AMERICAN    BOOK    COMPANY 


:< 


PRESIDENT     HILL'S    TEXT-BOOKS 


ISt. 

THE     ELEMENTS     OF     RHETORIC 
AND     COMPOSITION. 

ad. 

THE     SCIENCE     OF     RHETORIC. 

30- 
THE    ELEMENTS    OF    LOGIC. 


Copyright,  1883,  by  Sheldon  &•  Co. 


^^^'^    'i^  J  '1^  '1^  'i^ 


B"2r    TliB    EIDITOIt. 


Although  there  are  many  elementary  works  on 
Logic,  it  has  been  for  a  long  time  felt  that  there  is 
no  text-book  that  precisely  meets  the  wants  of  our 
colleges  and  normal  schools.  The  nearest  approach  to 
the  desideratum  is  the  "Elementary  Lessons  ia  Logic" 
which  constitutes  the  substance  of  this  book.  Its 
merits  are  its  fresh  treatment  of  the  subject,  its  ful- 
ness and  felicity  of  illustration,  its  clearness  and  vigor 
of  style,  its  recognition  of  the  logical  methods  of 
science  as  a  part  of  Logic,  and  its  comprehensive  pre- 
sentation of  recent  views  on  the  subject  of  reasoning. 
It  was  designed  by  its  author,  Professor  W.  Stanley 
Jevons,  as  a  hand-book  for  students  in  the  English 
Universities.  It  is  this  alone  that  has  stood  in  the 
way  of  its  general  adoption  as  a  text-book  in  this 
country,  for  the  methods  of  study  in  England  and 
America  are  essential'iy  difffirent.  In  England  the 
student  reads  under  the  direction  of  a  Tutor  and  thua 
prepares  himself  for  a  public  examination.  In  America 
daily  recitations  on  the  topical  plan  are  almost  univsr- 


tf  PREFACE. 

sal  in  the  study  of  this  subject.  Although  Professoi 
Jevoiis  divided  his  work  iuto  Lessons,  these  bore  no 
relation  to  the  amount  usually  assigned  for  a  daily  les- 
son, and  so  failed  to  provide  that  distribution  of  the 
matter  that  is  desirable  for  the  class-room.  It  is  also  a 
defect  of  this  method  of  dividing  a  subject  that  it  fails 
to  present  the  logical  relations  of  parts  and  the  organic 
unity  of  the  whole.  But  the  chief  defect  of  the  original 
work,  as  a  text-book  for  classes  using  the  topical 
method,  is  the  want  of  an  exact  analysis  of  the  topics 
and  a  discrimination  of  that  which  is  essential  and 
should  be  firmly  fixed  in  the  memory,  from  that  which 
is  merely  explanatory  and  illustrative  and  needs  only  to 
be  carefully  read  and  comprehended.  The  amount  of 
illustration  is  superabundant  in  some  cases,  and  tends 
to  distract  the  mind  and  render  it  less  attentive  to 
gteat  principles  than  is  consistent  with  a  firm  grasp  of 
such  a  science.  The  amount  of  matter  in  the  book, 
unless  a  i>art  be  subordinated,  is  too  great  to  be 
mnstcnHl  in  the  single  term  that  is  usually  given  to  the 
gtudy  even  in  the  highest  grade  of  schools  in  this 
conntry. 

The  publishers  have  been  led  to  believe  from  the  rep- 
resent at  ions  of  professors  of  Tjogic  who  have  had  exten- 
sive exi>crienco  in  teaching  the  science,  that  a  recasting 
of  Professor  .Tcvons'  work,  with  special  reference  to  the 
difficulties  enumenitod  above,  would  render  it  in  every 
respect  adapted  to  meet  the  confessed  demand  for  a 
thorough  tcxt-l»ook  on  this  subject.  It  would  have 
been  most  desirable  if  Professor  Jevons  himself  might 
have  reca'^t  the  book  with  these  considerations  in  mind, 
but  that  was  rendered  impossible  by  his  sudden  death 


PBEFAOB.  T 

by  di'owning.  In  attempting  to  adapt  this  admirable 
treatise  to  the  needs  of  American  students,  I  have 
sought  to  make  the  following  changes  : 

1.  To  introduce  a  complete  and  precise  Analysis, 
and  to  distribute  the  text  in  such  a  manner  as  to 
render  the  method  and  arrangement  of  the  book  as 
lucid  as  possible. 

3.  To  give  prominence  to  cardinal  principles  and 
important  doctrines  by  stating  them  in  large  type, 
while  matter  that  is  simplj*  explanatory  and  illustrative 
is  subordinated  by  being  thrown  into  smaller  type. 

3.  To  impart  to  the  treatment  of  Inductive  Logic 
more  system  and  co-ordination  than  are  found  in  the 
original  work. 

4.  To  give  unity  to  the  treatment  of  the  subject  by 
placing  the  discussion  of  Recent  Logical  Views  at  the 
end  of  the  text,  instead  of  near  the  middle  of  the  book, 
thus  avoiding  a  break  in  the  continuity  of  the  better 
established  doctrines  of  the  science. 

5.  To  facilitate  reviews  by  placing  at  the  end  of 
each  section  a  summary  of  the  topics  treated  of  in 
that  section. 

6.  To  impart  some  information  concerning  writers 
on  Logic  named  in  the  text,  of  whom  the  average 
student  cannot  be  presumed  to  have  any  exact  knowl- 
edge. This  information  is  inserted  in  the  Index  and 
Glossary  under  the  names  of  the  writers  referred  to. 

I  have  for  the  most  part  retained  the  language  of  the 
author,  only  adding  where  addition  seemed  to  be 
necessary  to  clearness.  Such  errors  and  infelicities  of 
expression  as  I  have  noticed,  I  have  corrected.     The 


yi  PREFACE. 

singular  clearness  of  Professor  Jevons's  mind,  however, 
has  rendered  the  occurrence  of  these  infrequent. 

Although  the  opinion  of  teachers  may  vary  upon  this 
point,  the  plan  of  requiring  a  close  reproduction  of  the 
text  in  large  print,  with  questioning  upon  the  matter 
in  the  small  'type,  will  probably  commend  itself  in 
practice.  In  the  review  the  parts  in  small  type  might 
be  omitted.  Questions  for  examinations  are  inserted 
at  the  end  of  the  book. 

In  the  hope  that  the  work  as  recast  may  be  found 
useful  to  teachers  and  students,  this  revision  is  offered 
to  the  public. 

The  Editor. 


A    SKETCH 


OF 


THE    AUTHOR'S     LIFE. 


WILLIAM  STANLEY  JEVONS  was  born  in  Liverpool,  in 
September,  1835.  His  father,  Thomas  Jevons,  was  an  iron  mer- 
chant, and  bis  mother  was  a  daughter  of  William  Roscoe,  the 
banker  and  historian. 

Having  obtained  his  early  education  at  the  High  School  of 
Liverpool  and  at  the  Mechanics'  Institution,  at  the  age  of  sixteen 
he  entered  University  College,  London.  There  he  became  so 
distinguished  in  mathematics  and  chemistry  that  at  the  age  of 
nineteen,  while  still  an  undergraduate,  he  was  invited  to  a  posi 
tion  in  the  Sydney  Mint,  Australia.  He  accepted  this  appoint- 
ment, but  after  five  years'  residence  in  Australia,  he  returned  to 
London,  completed  his  course  of  study  and  took  the  Master's 
degree.  He  attained  the  highest  honors  in  Logic,  Moral  Phil- 
osophy and  Political  Ekx)nomy. 

In  1863  Jevons  began  his  work  as  a  teacher  in  Owens  College, 
Manchester,  and  three  years  later  was  elected  Professor  of  the 
three  studies  in  which  he  especially  excelled.  After  ten  years  of 
distinguished  service  at  Manchester,  during  which  period  he  won 
an  extended  reputation  as  a  writer,  Professor  Jevons  felt  the 
burden  of  his  varied  duties  to  be  too  heavy  for  him  and  accepted 


viii  AUTHOR'S    LIFE. 

the  chair  of  Political  Fkx)nomy  in  University  College,  London. 
Even  the  duties  of  thio  |>osition,  thougli  not  extensive,  became 
oppn>ssive  to  liiin  witli  hcaltli  tliat  had  grown  uncertain,  and  in 
the  wint«'r  of  1880-1  he  retired  U)  private  life. 

Hi8  life  was  teriniaatcd  by  an  accident  on  the  13th  of  August, 
1882,  while  bathing  at  Galley  Hill,  on  the  Sussex  coast.  The 
precise  cauw  of  his  death  in  the  water  is  not  known,  but  it  is 
suppoBcKl  that  in  his  feeble  health  he  was  not  able  to  resist  the 
ni'rvous  shock  caused  by  the  excitement  of  bathing,  and  being 
disabled  he  was  drowned. 

As  a  writer  Professor  .levons  was  remarkably  fertile.  In 
addition  to  the  present  work,  he  produced  on  the  subject  of  logic 
three  notable  books.  A  work  entitled  "  Pure  Ix)gic"  was  pub- 
lished in  1864.  "The  Substitution  of  Similars"  (1869)  was  an 
attempt  to  simplify  all  reasoning  by  referring  it  to  a  single 
principle  more  coraj)rehensive  than  Aristotle's  dicta.  "  The 
Principles  of  Science "  (1874)  was,  in  effect,  the  application  of 
this  princi|»le  to  the  details  of  scientific  method,  and  anex()Osition 
of  the  fundamental  postulates  on  which  all  human  science  rests. 
Both  works  have  called  forth  considerable  controversy,  but  the 
latt<'r  in  particular  has  been  useful  in  the  direction  of  scientific 
reasoning.  More  r<*cently  Professor  Jevons  has  reviewed  with 
nearchinfr  criticism  the  logical  work  of  the  late  John  Stuart  Mill. 
Referring  to  hin  treati.ses  on  I.rf)gic  and  his  review  of  Mill,  the 
"  Rrvui-  Philowiphique"  ways:  "  His  gre^t  work  '  The  Principles 
of  Scionfj' •  and  hi.i  recent  i>olomic  against  the  Logic  of  Stuart 
Mill  have  givr-n  him  a  (ii>-tiiiguished  rank  among  English 
l«>giriann."  The  name  notice  hIho  mlds  that  "the  elementary 
works  of  Siaiili-y  Jevons  have  b«H!f)m('  classic." 

We  cannot  properly  c\on>-  this  sketch  without  a  brief  reference 
to  Pmfe.^«<.r  Jevons'  works  on  Political  Economy,  to  which  he 
devoU<d  many  of  hiti  »>est  yc^n.     The  roost  popular  of  these  are 


AUTHOR'S   LIFE.  IX 

The  "  ITieory  of  Political  Economy  "  (1871),  an  attempt  topresenl 
the  subject  under  a  mathematical  form  ;  *'  Money  and  the  Mecb 
anism  of  Exchange  "  (1875),  a  more  popular  presentation  of  the 
subject,  being  a  contribution  to  the  International  Scientific 
Series ;  and  "  The  Primer  of  Political  Economy  "  (1878),  a  greatly 
simplified  introduction  to  tlie  subject.  A  more  special  and 
technical  production  is  the  work  on  "  The  Coal  Question." 

"As  a  man,"  says  the  Editor  of  the  English  periodical  Mind, 
"Jevons  was  most  lovable.  Of  a  shy  and  retiring  disposi- 
tion, he  never  mixed  much  in  general  society,  but  he  bad  a 
geniality  of  nature  and  sweetness  of  temper,  with  a  ready  help- 
fulness, which  secured  him  an  inner  circle  of  most  devoted 
friends.  With  so  firm  a  grasp  as  he  had  of  his  own  convictions 
and  opinions,  he  was  admirable  for  the  spirit  in  which  he  courted 
ftnd  welcomed  criticism." 

In  recognition  of  his  attainments  Professor  Jevons  was  made 
a  Fellow  of  the  Royal  Society,  and  the  honorary  degree  o^ 
Doctor  of  Laws  was  conferred  upon  him  by  the  University 
of  Edinburgh.  The  highest  authorities  in  Europe  accord  to  him 
"an  assured  reputation  as  an  original  thinker  and  writer  in  th« 
two  departments  of  Logic  and  Political  Economy." 

Tbs  Editor. 


INTRODUCTION. 


PASB 

1.  Definition  OP  Logic 1 

2.  Natuke  of  a  Law  of  Thought 3 

8.  A  Science  of  Thought  Possible 8 

4.  Distinction  between  Fokm  and  Matter 5 

5.  Logic  a  General  Science 6 

6.  The  Particular  Sciences,  Special  Logics. 6 

7.  Logic  BOTH  A  Science  AND  AN  Art 7 

8.  The  Usefulness  of  Logic 8 

9.  Analysis  op  an  Argument 9 

10.  Theories  of  the  Real  Subject-matter  op  IjOgic 10 

11.  The  Three  Logical  Operations  of  Mind 13 

12.  Method  op  Treatment 16 


OHAPTEE    I 
TERMS. 

SECTION  «.— THE  VARIOUS  KINDS  OF  TERMS 

1.  The  Meaning  op  '"  Term"  Explained 17 

2.  Categorematic  and  Syncategorematic  Word.^ 18 

B.  Singular  Terms 20 

4.  General  Terms 20 

5.  Collective  Terms 21 

6.  Concrete  and  Abstract  Terms  28 


Xli  ANALYSIS. 

rASB 

7    POBITITE  AND  NEGATIVK  TERMS 24 

8.  Tkiv  ^TiVK  Tkums ..26 

9.  Uelative  AND  Absolute  Terms 27 

10.  SOMMAllY 28 

SECTION   II.— THE  AMBIGUITY  OF  TERMS. 

1.  Importance  op  Avoiding  Ambiguity 80 

2.  Univocal  AND  EquivocAi,  Terms 81 

8.  Kinds  AND  Causes  OK  Ambiguity 88 

SECTION    III.— EXTENSION    AND    INTENSION. 

1.  Imfortancb  of  Undicrstandino  this  Double  Mean- 

ing   39 

2.  Meaning  of  Extension  and  Intension 39 

8.  Various  Forms  of  Expressing  Extension  and  Inten- 
sion    41 

4.  The  Variation  of  Extension  and  Intension 42 

6.  The  Law  OF  Variation 42 

C.  Connotative  AND  Non-connotatxve  Terms 43 

SECTION    IV.-THE  GROWTH   OF   LANGUAGE. 

1    The  Two  Principal  Processes  of  Growth 46 

2.  (Jknkuai.ization         47 

3.  Specialization 50 

4    Dkhynonymization 51 

5.  Mktapiioukai,  Extension  of  Meaning 52 

fl   Origin  ok  TiiK  Mkntal  ViK'ABULARY 53 

7.  The  Fertility  ok  I{oot  words 54 

SECTION    V  -THE    PERFFCT   AND    THE    IMPERFECT 
KNOWLEDGE   OF  TERMS. 

1.  &rATF.MKNT  OF  THE  QtrKSTION 66 

2.  8(  IIKMK  OK    DiHTINCTIONs 56 

8.  The  Intuitivk  and  Svmholk  MtmioDs  Compared 02 


ANALYSIS.  XIU 

CHAPTER    II. 
PROPOSITIONS. 

SECTION  I.— THE   KINDS   OF   PROPOSITIONS. 

FAOB 

1.  Meaning  op  "Proposition "  Explained 64 

2.  Analysis  op  a  Proposition 65 

3.  Categorical  and  Conditional  Propositions 66 

4.  The  Quantity  and  Quality  op  Propositions 67 

5.  Aristotle's  View  of  Quantity 68 

6.  Names  of  the  Four  Propositions 70 

7.  Variations  prom  the  Logical  Form 71 

8.  The  Modality  of  Propositions 73 

SECTION    II.— THE  OPPOSITION  OF  PROPOSITIONS. 

1.  The  Four  Propositions  Explained 75 

3.  The  Distribution  op  Terms 79 

3.  Tablk  op  Results 80 

4.  Relations  of  the  Four  Propositions 80 

5.  The  Scheme  op  Opposition 83 

6.  The  Laws  of  Opposition 83 

7.  The  Conditions  OP  Opposition 84 

8.  The  Matter  op  Propositions 85 


SECTION    III.— CONVERSION    AND    IMMEDIATE 
INFERENCE. 

1.  The  Nature  op  Inference 86 

2.  Conversion  of  Propositions 87 

3.  Immediate  Inference 90 


xiT  ANALYSIS. 


SECTION    IV.— THE    LOGICAL    ANALYSIS  OF  SEN- 
TENCES. 

PAea 

1.  Relation  op  Logic  to  this  Topic 93 

2.  The  UiiAMMAritAL  and  tub  Logical  Predicate 94 

8  The  Pluralitv  of  Propositions  in  a  Sentence 95 

4.  Complex  Sentences  96 

6.  Modes  ok  Exhibiting  Constroction 99 


CHAPTER    III. 
SYLLOGISMS. 

SECTION  I— THE   LAWS   OF  THOUGHT. 

1.  The  Statement  of  tiik  Primary  Laws  of  Thought.  .  104 

2.  Explanation  of  TUK  Laws 105 

8.  The  Canons  ok  Syllogism  108 

4.  TuK  Axioms  ok  Mathematics  110 

8.  Aristotle's  Dicta Ill 

SECTION    II.  -THE   RULES  OF  THE  SYLLOGISM. 

1.  The  Dekinition  ok  "  Syllogism" 118 

2.  The  Mkanino  OK  "  MiDDLK  Term" 114 

8.  The  Csk  ok  Middle  Tkum  in  S^-llogism 114 

4.  Statkmknt  ok  thk  Rulks  of  Syi,logism 115 

5  Explanation  </K  thf:  Rules 116 

SECTION    III— THE   MOODS   AND   FIGURES   OF 
THE   SYLLOGISM. 

1.    EXPI.ANATION  ok  "  Mf)OD8" 124 

2    The  Number  ok  Valid  Moods 125 

8.    EZPLAKATION  OF  "  FIGURES  " 127 


ANALYSIS.  XV 

PASS 

4.  Thb  VaiiID  Moods  in  the  Different  Figures 128 

5.  Conclusions  Proved  in  the  Different  Figures 130 

SECTION    IV.— THE   REDUCTION    OF  SYLLOGISMS. 

1.  The  Mnemonic  Verses 133 

2.  Explanation  op  the  Mnemonic  Verses 134 

3.  Conclusions  from  Particular  Premises 139 

SECTION   v.— IRREGULAR   AND   COMPOUND 
SYLLOGISMS. 

1.  The  Irregular  Mode  op  Expressing  Inferences 141 

2.  Explanation  of  "  Enthymeme  " 142 

3.  Prosyllogisms  and  Episyllogisms 144 

4  Sorites 145 

5.  Syllogisms  in  Extension  and  in  Intension 148 

SECTION   VI.— CONDITIONAL   SYLLOGISMS. 

1.  Classification  op  Propositions 149 

2.  Antecedent  and  Consequent 150 

3.  Kinds  op  Hypothetical  Syllogisms 151 

4  The  Rule  for  Hypothetical  Syllogisms 152 

5.  The  Reduction  of  Hypothetical  to  Categorical 

Syllogisms 153 

6.  Fallacies  in  Hypothetical  Syllogisms 155 

7.  Disjunctive  Syllogisms 156 

8.  The  Dilemma 158 

CHAPTER  IV. 
FALLACIES. 

SECTION    I.— LOGICAL   FALLACIES. 

1.  Classification  op  Logical  Fallacies 162 

2.  The  Fallacy  op  Equivocation •  163 

3.  The  Fallacy  op  Amphibology 164 


4  Thb  Fauuact  OF  Composition 105 

6.  The  Fallacy  ok  Division •  168 

6.  The  Falijicy  of  Accident 167 

7  TiiK  Fallacy  of  the  Figuke  of  Speech. 168 

SECTION   II.— MATERIAL    FALUCIES. 

1.  The  Ci.a88ification  of  Material  Fallacies 169 

2.  TuE  Fallacy  of  Accidknt  and  its  Convekse 169 

3.  The  Fallacy  of  Iruelevant  Conclusion 171 

4.  The  Fallacy  of  Petitio  Principii 173 

5.  The  Fallacy  of  the  Consequent.  . .    175 

6.  The  Fallacy  of  False  Cause  175 

7.  The  Fallacy  of  Many  Questions 176 


CHAPTER    V, 
INDUCTION. 

SECTION   I.— THE   INDUCTIVE   SYLLOGISM. 

1.  Induction  and  Deduction  Contrasted 178 

2.  Explanation  ok  Traduction 179 

8.  Importance  ok  Induction 180 

4.    PKRFtXT  and  ImpERKE<T  INDUCTION 181 

8.  The  Dikkeuknce  between  Pkrfect  and  Imperfect 

iNouc-rioN     181 

6.  The  Perfect  Inouctivk  Syij.ooism 183 

7.  The  Peiikect  Inductivk  Svli.ooism  Disjunctive 184 

8   The  Imteuki-xt  Inductive  Svlixkusm . . .  184 

9.  The  Fundxmental  Assumition  of  Induction 186 

SECTION    II.— THE  FORMS   OF   INDUCTION. 

1   The  Cii aracter  of  the  Data 187 

2.  8PEt?iAL  Kinds  of  Induction 195 


ANALYSIS.  XTii 

CHAPTER    VI. 
METHOD. 

SECTION    I.— INDUCTIVE   METHOD. 

tAoa 

1.  The  Seakch  for  Facts 201 

2.  The  Rule  for  Observation 206 

8.  The  Uses  op  Hypothesis  and  Theory 208 

4.  Definitions  of  Terms  Employed  in  Investigation.  . .  212 
6.  Canons  op  Induction 215 

SECTION    II.— DEDUCTIVE   METHOD. 

1.  The  Predicables  287 

2.  Logical  Divisions 234 

8.  Dichotomy,  or  Exhaustive  Division 236 

4.  Definition 238 

5.  Classification 240 

6.  Requisites  of  a  Good  Classification 242 

7.  Denomination 245 

SECTION   III.— COMPLETE   METHOD. 

1.  Empirical  and  Rational  Knowledge 249 

2.  The  Elements  of  Complete  Method 251 

8.  The  Nature  of  Explanation 254 

4.  Pascal  on  Method 257 

6.  Descartes  on  Method 263 

CHAPTER    VII. 
RECENT   LOGICAL   VIEWS 

SECTION   I.— THE  QUANTIFICATION   OF  THE   PREDICATE 

1.  Meaning  of  the  Expression 4«M 

2.  Conversion  with  a  Quantified  Predicate 264 


Xriil  ANALYSIS. 

8.  The  Rulb  for  Contersiow 266 

4   NuMBEu  OP  Propositions  with  a  Quantified  Predi- 
cate  266 

5.  NcMBER  OF  Syllogisms  wmi  Quantified  Predicate.  268 

6.  Hamilton's  Notation 268 

7.  Hamilton's  Canon  of  the  Syllogism  270 

SECTION   II.— BOOLE'S    SYSTEM   OF   LOGIC. 

1,  The  Difficulty  of  Dr.  Boole's  Statement 272 

2.  Applk  ation  of  the  Law  of  Excluded  Middle 273 

8.  Application  of  the  Law  of  Contradiction 274 

4.  Universality  of  the  Method. 275 

5.  Comparative  Excellence  of  the  System 27? 

6.  Thb  Logical  Abacus  and  the  Logical  Machine 28(1 

Questions  AND  Exercises 283 

IXDKX  ANDULOWABT 314 


1.  Definition  of  Lo^c. 

Logic  may  be  most  briefly  defined  as  the  Science  of 
Reasoning.  It  is  more  commonly  defined,  however,  as 
the  Science  of  the  Laws  of  Thought,  and  some  lo- 
gicians think  ?.t  desirable  to  specify  still  more  accurately 
that  it  is  the  Science  of  the  Formal,  or  of  the  Necessary 
Laws  of  Thoughft.  Before  these  definitions  can  be  of 
any  real  use  to  us  we  must  come  to  a  clear  understand- 
ing as  to  the  meaning  of  the  expressions ;  and  it  will 
probably  appear  that  there  is  no  great  difEerence  be- 
tween them. 


The  name  of  logic  is  derived  from  the  common  Greek  word 
Aoyof,  which  usually, means  word,  or  the  sign  and  outward  mani- 
festation of  any  inward  thought.  But  the  same  word  was  also 
used  to  denote  the  inward  thought  or  reasoning  of  which  words 
are  the  expression,  and  it  is  thus,  probably,  that  later  Greek 
writers  on  reasoning,  were  led  to  call  their  science  i-ioT-qfir} 
XoytKT],  or  logical  science  ;  also  -exi'V  2.oyiKij,  or  logical  art.  The 
adjective  TioyiKr},  being  used  alone,  soon  came  to  be  the  name  of 
the  science,  just  as  Mathematic,  Rhetoric,  and  other  names 
ending  in"ic"  were  originally  adjectives,  but  have  been  con- 
verted into  substantivea 


INTROUUOTION. 


2.  Nature  of  a  l-.aw  of  Thought. 

By  a  Law  of  Thought  we  mean  a  certain  uniformitj 
or  agreenu'iit  which  exists  and  must  exist  in  the  modea 
in  which  all  persons  think  and  reason,  so  long  as  they 
do  not  make  what  we  call  mistakes,  or  fall  into  self- 
contradiction  and  fallacy.  The  laws  of  thought  are 
natural  laws  with  which  we  have  no  power  to  interfere, 
and  which  are,  of  course,  not  to  be  in  any  way  confused 
with  the  artificial  laws  of  a  country,  which  are  invented 
by  men  and  can  be  altered  by  them.  Every  science  is 
occupied  in  detecting  and  describing  the  natural  laws 
which  arc  inflexibly  observed  by  the  objects  treated  in 
the  science. 

The  science  of  astronomy  investigates  the  uniform  or  similar 
way  in  wliidi  the  iieavenly  bmiies,  and,  in  fact,  all  material  sub- 
Btanct!8,  tend  to  fall  towards  each  other,  as  a  stone  falls  towards 
the  earth,  or  to  move  round  each  other  under  the  influence  of 
this  tendency.  The  universal  law  of  gravitation  is  thus  th>' 
natural  law  of  uniformity  treated  in  physical  astronomy. 

In  chemistry  tlie  law  of  equivalent  proportions  describes  the 
well  ascertained  fact  that  each  chemical  substance  enters  into 
combination  with  every  other  chemical  substance  only  in  certain 
de6nite  proportions;  as  when  exactly  eight  jiarts  by  weight  of 
oTyg(!n  unite  with  one  part  of  hydrogen  to  form  water,  or 
sixteen  parts  of  oxygen  and  six  parts  of  carbon  unite  to  form 
cjirbonic  acid  in  the  ordinary  burning  of  a  flame  or  fire 
Whenever  we  can  detect  uniformities,  or  similarities,  we  so 
far  create  science  and  arrive  at  natural  laws.  But  there  may 
be  and  are,  many  things  so  fickle,  complicated,  and  uncertain, 
that  we  can  never  be  sure  we  have  detected  laws  that  they  will 
uniformly  r>bf'y  ;  ir  Huch  cases  no  science,  in  the  pro|)er  sense  of 
tlie  word,  is  j)088ible.  There;  is  no  such  thing,  for  instance,  as  a 
n-al  sricnre  of  human  character,  because  ti.e  human  mind  is  too 
variable  and  complicated  a  subject  of  investigation.    There  are 


nrTRODUCTIOlC.  3 

no  two  penons  so  mucli  alike  that  70a  may  be  sare  of  one  acting 
in  all  circumstances  as  the  other  would  ;  it  thus  becomes  impossi- 
ble to  arrange  persons  in  classes  so  that  all  who  are  in  the  same 
class  shall  act  uniformly  in  the  same  manner  in  any  given  cir 
jumstancea 


3.  A  Science  of  Thought  Possible. 

There  is  a  science  of  human  reason,  or  thought,  apart 
from  the  many  other  acts  of  mind  which  belong  to  human 
character,  because  there  are  modes  iu  which  all  persons 
do  uniformly  think  and  reason,  and  must  think  and 
reason.  Thus,  if  two  things  are  identical  with  a  third 
common  thing,  they  are  identical  with  each  other. 
This  is  a  law  of  thought  of  a  very  simple  and  obvious 
character,  and  we  may  observe  concerning  it : — 

(1)  That  all  people  think  in  accordance  with  it, 
and  agree  that  they  do  so  as  soon  as  they  understand  its 
meaning. 

(2)  That  they  think  in  accordance  with  it  whatever 
may  be  the  subject  about  which  they  are  thinking. 

Thus,  if  the  things  considered  are — 

London, 

The  Metropolis, 

The  most  populous  city  in  Great  Britain, 

since  "the  Metropolis  is  identical   with  London,"  and  "London 
is  identical  with   the  most  populous  city  in  Great  Britain,"  it 
follows,  necessarily,  in  all  minds,  that  "  the  Metropolis  is  identi- 
cal with  the  most  populous  city  in  Great  Britain." 
Again,  if  we  compare  the  three  following  things — 

Iron, 

The  most  useful  metal. 

The  cheapest  metal, — 

And  it  be  allowed  that  "  The  most  useful  metal  is  Iron,"  and 


4  iin^ODUcnoN. 

"Iron  is  the  cheapest  metal,"  it  follows,  necessarily,  in  all 
minds,  that  "  the  moat  useful  metal  is  the  cheapest."  VV^e  here 
have  two  examples  of  the  general  truth,  that  things  identical 
with  the  same  thing  are  identical  with  each  other;  and  this,  we 
may  say,  is  a  general  or  necessary  form  of  thought  and  reasoning. 
Compare,  again,  the  following  three  things:— 

The  earth, 

Planets, 

Bodies  revolving  in  elliptic  orbits. 

We  cannot  say,  as  before,  that  "  the  earth  is  identical  with  the 
planets ; "  it  is  identical  only  with  one  of  the  planets,  and  we 
therefore  say  that  "it  is  a  planet."  Similarly  we  may  say  that 
"  the  planets  arc  bodies  revolving  in  ellipti"  orbits,"  but  only  a 
part  of  ihe  whole  number  so  revolving.  Nevertheless,  it  follows 
that  if  the  earth  is  among  the  planets,  and  the  planets  among 
bodies  revolving  in  elliptic  orbits,  then  the  earth  is  among  the 
latter. 

A  very  elementary  knowledge  of  cheraistiy  enables  us  to 
argue  similarly  concerning  the  following : — 

Iron, 

Metals, 

Elementary  substances. 

Iron  is  one  of  the  metals,  and  metals  are  elements  or  simple 
undfcomposable  substances,  in  the  sense  of  being  among  them 
or  a  part  of  them,  but  not  as  composing  the  whole.  It  follows, 
nect-ssarily,  tliat  "Iron  is  one  of  the  elementary  substances." 
We  have  had,  then,  two  examples  of  a  fixed  and  necessary  form 
of  thouglit,  which  is  necessary  and  true,  whatever  the  things 
may  be  to  whicli  it  is  a])|ilied.  The  form  of  argument  may  be 
expressed  in  several  different  ways,  and  we  shall  have  to  con- 
sider it  minutely  in  the  lessons  on  the  syllogism.  We  may 
express  it,  for  instance,  by  saying  that  "  part  of  a  part  is  part 
of  the  whole."  Iron  is  part  of  the  class  of  metals,  which  is  part 
of  the  class  of  elements — hence  iron  is  part  of  the  class  of 
elements. 


IlfTBODUOnON. 


4.  Distinction  between  Form  and  Matter. 

In  order  to  apprehend  the  meaning  of  the  expression, 
"  the  necessary  forms  of  thought,"  we  must  distinguish 
between  form  and  matter.  A  form  is  something  which 
may  remain  uniform  and  unaltered,  while  the  matter 
thrown  into  that  form  may  be  varied.  Medals  struck 
from  the  same  dies  have  exactly  the  same  form,  but 
they  may  be  of  various  matter,  as  bronze,  copper,  gold, 
or  silver.  A  building  of  exactly  the  same  form  might 
be  constructed  either  of  stone  or  bricks ;  furniture  of 
exactly  similar  shape  may  be  made  of  oak,  mahogany, 
walnut  wood,  etc.  Just  as  we  thus  famiharly  recognize 
the  difference  of  form  and  substance  in  common  tangi- 
ble things,  so  we  may  observe  in  Logic,  that  the  form 
of  an  argument  is  one  thing,  quite  distinct  from  the 
various  subjects  or  matter  which  may  be  treated  in  that 
form. 

We  may  almost  exhibit  to  the  eye  the  form  of  reasoning  to 
which  belong  our  two  latter  arguments,  as  follows : — 

(Y) 


(X)....is....(Z) 

If  within  the  three  pairs  of  brackets,  marked  respectively  X, 
T  and  Z,  we  place  three  names,  such  that  the  one  in  place  of  X 
may  be  said  to  come  under  that  in  T.  and  that  in  Y  under  that 
in  Z,  then  it  necessarily  follows  that  the  lirst  lX)  comes  undei 
the  last  iZ). 


INTBODUCTION. 


5.  Lo^ic  a  General  Science. 

Logic,  then,  is  the  science  occupied  in  ascertaining 
and  descnbing  ail  the  general  forms  of  thought  which 
we  must  employ  so  long  as  we  reason  validly.  These 
forms  are  very  numerous,  although  the  principles  on 
which  they  are  constructed  are  few  and  simple.  It  will 
hence  appear  that  logic  is  the  most  general  of  all  the 
sciences.  Its  aid  must  be  more  often  required  than  the 
aid  of  any  other  science,  because  all  the  particular 
sciences  treat  portions  only  of  existing  things,  and 
create  very  different  and  often  unconnected  branches  of 
knowledge.  But  logic  treats  of  those  principles  and 
forms  of  thought  which  must  be  employed  in  every 
branch  of  knowledge.  It  treats  of  the  very  origin  and 
foundations  of  knowledge  itself ;  and  though  it  is  true 
that  the  logical  method  employed  in  one  science  may 
differ  somewhat  from  that  employed  in  another  science, 
yet,  whatever  the  particular  form  may  be,  it  must  be 
logical,  and  must  confonn  to  the  laws  of  thought. 
There  is,  in  short,  something  in  which  all  sciences  must 
be  similar  ;  to  which  they  must  conform  so  long  as  they 
maintain  what  is  true  and  self-consistent;  and  the 
work  of  logic  is  to  explain  this  common  basis  of  all 
Bcicnce. 

6.  The  Particular  Sciences,  Special  Logics. 

One  name  which  has  been  given  to  Logic,  namely, 
the  Science  of  Sciences,  very  aptly  describes  the  all 
extensive  power  of  logical  principles.  The  cultivators 
of  8|)ecial  branches  of  knowledge  appear  to  have  been 
'ully  aware  of  the  allegiance  they  owe  to  the  highest  of 


DTrBODUCnON.  7 

the  sciences,  for  they  have  usually  given  names  imply, 
ing  this  allegiance.  The  very  name  of  logic  occurs  aa 
part  of  nearly  all  the  names  recently  adopted  for  the 
sciences,  which  are  often  vulgarly  called  the  "ologies," 
but  are  really  the  "  logics,"  the  "  o  "  being  only  a  con- 
necting vowel  or  part  of  the  previous  word.  Thus, 
geology  is  logic  applied  to  explain  the  formation  of  the 
earth's  crust ;  biology  is  logic  apphed  to  the  phenomena 
of  life ;  psychology  is  logic  applied  to  the  nature  of  the 
mind  ;  and  the  same  is  the  case  with  physiology,  ento- 
mology, zoology,  teratology,  morphology,  anthropology, 
theology,  ecclesiology,  thalattology,  and  the  rest.*  Each 
science  is  thus  distinctly  confessed  to  be  a  special  logic. 

7.  Logic  both  a  Science  and  an  Art. 

Much  discussion  of  a  somewhat  trifling  character  has 
arisen  upon  the  question  whether  Logic  should  be  con- 
sidered a  science  only,  an  art  only,  op  both  at  the 
same  time.  Sir  W.  Hamilton  has  even  taken  the 
trouble  to  classify  almost  all  the  writers  on  logic  ac- 
cording as  they  held  one  opinion  or  the  other.  But  it 
seems  substantially  correct  and  suflScient  to  say,  that 
logic  is  a  science  in  so  far  as  it  merely  investigates  the 
necessary  principles  and  forms  of  thought,  and  thus 
teaches  us  to  understand  in  what  correct  thinking  con- 
sists ;  but  that  it  becomes  an  art  when  it  is  occupied  ir 
framing  rules  to  assist  persons  in  detecting  false  reason- 
iusr. 


*  Except  Philology,  which  is  differently  formed,  and  means  the  love  OJ 
etudy  of  words;  the  name  of  tlu8  science,  if  formed  upon  the  same  plan, 
would  be  logolog^ 


t  nn-RODucrnoN. 

A  science  teaches  us  to  know  and  an  art  to  do,  and  all  tb« 

moie  perfect  Bciences  lead  to  the  creation  of  corresponding  usefui 
arts.  Astronomy  is  the  foundation  of  the  art  of  navigation  on  the 
ocean,  as  well  as  of  the  arrangement  of  the  calendar  and  chronol- 
ogy. Physiology  is  the  basis  of  the  art  of  medicine,  and  chemistry 
is  the  iMisis  of  many  useful  arts.  Logic  lias  similarly  been  con- 
Bidered  hs  the  basis  of  an  art  of  correct  reasoning  or  investigation 
which  should  teach  the  true  method  to  be  observed  in  all 
sciences.  The  celebrated  British  logician,  Duns  Scotus,  who 
lived  in  the  13th  century,  and  called  logic  the  Science  of 
Sciences,  called  it  also  the  Art  of  Arts,  expressing  fully  its 
pre-eminence.  Others  have  thus  defined  it — "  Logic  is  the  art 
of  directing  the  reason  aright  in  acquiring  the  knowledge  of 
things,  for  the  instruction  both  of  ourselves  and  others."  Dr. 
Isaac  Watts,  adopting  this  view  of  logic,  called  his  well-known 
work  "  The  Art  of  Thinking." 

It  may  be  fairly  snid,  however,  that  Logic  has  more  the  form 
of  a  science  than  of  an  art,  for  this  reason  —  ail  persons 
necessarily  acquire  the  faculty  and  habit  of  reasoning  long  before 
^ley  even  know  the  name  of  logic.  This  they  do  by  the  natural 
exertion  of  the  powers  of  mind,  or  by  constant  but  unconscious 
imitation  of  others.  They  thus  observe  correctly,  but  uncon- 
sciously, the  principles  of  the  science  in  all  very  simple  cases. 
But  the  contradictory  opinions  and  absurd  fallacies  which  are 
put  forth  by  uneduc«ted  persons  show  that  this  unaided  exercise 
of  mind  is  not  to  be  trusted  when  the  subject  of  discussion 
presents  any  difficulty  or  complexity. 

8.  The  UseAiliiess  of  Log^c. 

The  study  of  logic,  then,  cannot  be  useless.  It  not 
only  explains  the  principles  on  which  every  one  has 
often  reasoned  correctly  before,  but  points  out  the 
dangers  which  e.xist  of  erroneous  argument.  The 
rcasoner  thus  becomes  consciously  a  correct  reasoner 
and  leanis  consciously  to  avoid  the  snares  of  fallacy. 
To  6ay  that  men  can  reason  well  without  logical  science 


INTRODUCTION.  t 

I's  about  as  trne  as  to  say  that  they  can  live  healthily 
without  medicine.  So  they  can — as  long  as  tliey  are 
healtliy  ;  and  so  can  reasoners  do  without  the  science  of 
leasoning — as  long  as  they  do  reason  correctly ;  but  how 
many  are  there  that  can  do  so  ?  As  well  might  a  man 
claim  to  be  immortal  in  his  body  as  infallible  in  his 
mind. 

And  if  it  be  requisite  to  say  a  few  words  in  defence 
of  Logic  as  an  art,  because  circumstances  in  the  past 
history  of  the  science  have  given  rise  to  misapprehen- 
sion, can  it  be  n<?cessary  to  say  anything  in  its  praise 
as  a  science?  Whatever  there  is  that  is  great  in  science 
or  in  art  or  m  literature,  it  is  the  work  of  intellect.  In 
bodily  form  man  is  kindred  with  the  brutes,  and  in  his 
perishable  part  he  is  but  matter.  It  is  the  possession  of 
sonscious  intellect,  the  power  of  reasoning  by  general 
notions,  that  raises  him  above  all  else  upon  the  earth ; 
and  who  can  say  that  the  nature  and  procedure  of  this 
intellect  is  not  almost  the  highest  and  most  interesting 
subject  of  study  in  which  we  can  engage  ?  In  vain 
would  any  one  deny  the  truth  of  the  favorite  aphorism 
of  Sir  "W.  Hamilton — 

In  the  world  there  is  nothing  great  but  man. 
In  man  there  is  nothing  great  but  mind. 

9.  Analysis  of  an  Argument. 

It  has  been  explained  that  Logic  is  the  Science  of 
Reasoning,  or  the  Science  of  those  Necessary  Laws  of 
Thought  which  must  be  observed  if  we  are  to  argue 
consistently  with  ourselves  and  avoid  self-contradiction. 
Argument  or  reasoning,  therefore,  is  the  strictly  proper 


10  nrrRODuoTioN. 

subject  before  us.  But  the  most  convenient  and  usual 
mode  of  studying  logic  is  to  consider  first  the  compo- 
nent parts  of  which  any  argument  must  be  made  up 
Just  as  an  architect  must  be  acquainted  with  the  ma- 
terials of  a  building,  or  a  mechanic  with  the  materials 
of  a  machine,  before  he  can  pretend  to  be  acquainted 
with  its  construction,  so  the  materials  and  instruments 
with  which  we  must  operate  in  reasoning  are  suitably 
described  before  we  proceed  to  the  actual  forms  0/ 
argument. 
If  we  examine  a  simple  argument  such  as  this— 

Iron  is  a  metal, 
Every  metal  is  an  element, 
Therefore  Iron  is  an  element, — 

we  see  that  it  is  made  up  of  three  statements  or  asser- 
tions, and  that  each  of  these  contains,  besides  minor 
words,  two  nouns  substantive  or  names  of  things,  and 
the  verb  "  is."  In  short,  two  names,  or  terms,  when 
connected  by  a  verb,  make  up  an  assertion  or  proposi- 
tion ;  and  three  such  propositions  make  up  an  argument, 
called  in  this  case  a  syllogism.  Hence  it  is  natural  and 
convenient  fii-st  to  describe  terms,  sis  the  simplest  parts; 
next  U)  proceed  to  the  nature  and  varieties  of  proposi- 
tions constructed  out  of  them,  and  then  we  shall  be  in 
A  position  to  treat  of  the  syllogism  as  a  whole.  Such, 
acconlingly,  are  the  three  parts  of  logical  doctrine. 

10.  Theories  of  the  Real  Subject-matter  of 
Logic. 

Rut  though  we  may  sjiy  that  the  three  parts  of  logic 
are  conrcrned  with  terms,  propositions,  and  syllogisms. 


INTBODUCTIOK.  11 

it  may  be  said,  with  equal  or  greater  truth,  that  thu 
acts  of  mind  indicated  by  those  forms  of  language  are 
the  real  subject  of  our  consideration.  The  opinions, 
or  rather,  perhaps,  the  expressions,  of  logicians  have 
varied  on  this  point.  Archbishop  Whately  says  dis 
tinctly  that  logic  is  entirely  conversant  about  language ; 
Sir  W.  Hamilton,  Mr,  Mansel,  aiul  most  other  logicians 
treat  it  as  concerned  with  the  acts  or  states  of  mind 
indicated  by  the  words ;  while  Mr.  J.  S.  Mill  goes  back 
to  the  things  themselves  concerning  which  we  argue. 
Is  the  subject  of  logic,  then,  language,  thought,  or  ob- 
jects ?  The  simplest  and  truest  answer  is  to  say  that  it 
treats,  in  a  certain  sense,  of  all  three.  Inasmuch  as  no 
reasoning  process  can  be  explained  or  communicated  to 
another  person  without  words,  we  are  practically  limited 
to  such  reasoning  as  is  reduced  to  the  form  of  language. 
Hence  we  shall  always  be  concerned  with  words,  but 
only  so  far  as  they  are  the  instruments  for  recording 
and  referring  to  our. thoughts.  The  grammarian  also 
treats  of  language,  but  he  treats  it  as  language  merely, 
and  his  science  terminates  with  the  description  and  ex- 
planation  of  the  forms,  varieties,  and  relations  of 
words.  Logic  also  treats  of  language,  but  only  as  the 
necessary  index  to  the  action  of  mind. 

Again,  so  long  as  we  think  correctly,  we  must  think  of  thinfjs 
as  they  are.  The  state  of  mind  within  us  must  correspond  to 
the  state  of  things  without  us,  whenever  an  opportunity  arise* 
for  comparing  them.  It  is  impossible  and  inconceivable  that  iron 
should  prove  not  to  be  an  elementary  substance,  if  it  be  a  metal, 
and  every  metal  be  an  element.  We  cannot  suppose,  and  there 
is  no  reason  to  suppose,  that  by  the  constitution  of  the  mind  we 
are  obliged  to  think  of  things  differently  from  the  manner  in 
which  they  are.      If,  then,  we  may  assume  that  things  really 


It  nrrRODucxiou. 

Agree  or  differ,  according  as  by  correct  logical  thought  we  are  In- 
duced to  believe  they  will,  it  does  not  seem  that  the  views  of  the 
logicians  named  are  irreconciieable.  We  treat  of  things  so  far 
•a  they  are  the  objects  of  tiiought,  and  we  treat  of  language  so 
far  as  it  is  the  emlxxliment  of  tiiought.  If  the  learner  will  bear 
this  explanation  In  mind,  he  will  be  saved  from  some  perplexity 
when  he  proceeds  to  read  different  works  on  logic,  and  finds  them 
to  vary  exceedingly  in  the  mode  of  treatment,  or  at  least  of  ex- 
pression. 

11.  The  Three  Logrical  Operations  of  Mind. 

If,  when  reduced  to  language,  there  be  three  parts  of 
logic,  terms,  projx)sition8,  and  syllogisms,  there  must  be 
as  many  different  kinds  of  thought  or  operations  of 
mind.    These  are  usually  called — 

(1)  Simple  apprehension. 

(2)  Judgment 

(3)  Reasoning,  or  discourse. 

(1)  Simple  Apprehension  is  the  act  of  mind  by 
which  wc  merely  Ixconie  aware  of  something,  or  have 
an  idea  or  impression  of  it  brought  into  the  mind.  The 
adjective  simple  means  apart  from  other  things,  and 
apprehension  the  taking  hold  by  the  mind.  Thus  the 
name  or  term  iron  instantaneously  makes  the  mind 
think  of  a  strong  and  very  useful  metal,  but  does  not 
tell  us  anything  about  it,  or  compare  it  with  any  thing 
else.  The  words  .<«/;/,  Jupiter,  Sirins,  St.  J'anVs  Cathe- 
dral, arc  also  terms  which  call  up  into  the  mind  certain 
well-known  objects,  which  dwell  in  our  recollection  even 
when  thoy  are  not  present  to  our  senses.  In  fact,  the 
use  of  a  term,  such  jis  those  j^iven  as  examples,  is 
merely  Jis  u  substitute  for  the  exhibition  of  the  actual 
things  named. 


INTBODUCnON.  18 

(2)  Judgment  is  a  different  action  of  mind,  and  con- 
sists  in  comparing  together  two  notions  or  ideas  of  ob- 
jects derived  from  simple  apprehension,  so  as  to  ascer. 
tain  whether  they  agree  or  differ.  It  is  evident,  there- 
fore, that  we  cannot  judge  or  compare  unless  we  are  con- 
scious of  two  things,  or  have  the  notions  of  two  things 
in  the  mind  at  the  same  time.  Thus,  if  I  compare  Jupiter 
and  Sirius,  I  first  simply  apprehend  each  of  them  ;  but, 
bringing  them  into  comparison,  I  observe  that  they 
agree  in  being  small,  bright,  shining  bodies,  which  rise 
and  set  and  move  round  the  heavens  with  apparently 
equal  speed.  By  minute  examination,  however,  I  no 
tice  that  Sirius  gives  a  twinkling  or  intermittent  lights 
whereas  Jupiter  shines  steadily.  More  prolonged  oij- 
servation  shows  that  Jupiter  and  Sirius  do  not  really 
move  with  equal  and  regular  speed,  but  that  the  former 
changes  its  position  upon  the  heavens  from  night  to 
night  in  no  very  simple  manner.  If  the  comparison  be 
extended  to  others  of  the  heavenly  bodies  which  are  ap- 
prehended or  seen  at  the  same  time,  I  shall  find  that 
there  are  a  multitude  of  stars  which  agree  with  Sirius 
in  giving  a  twinkling  light  and  in  remaining  perfectly 
fixed  in  relative  position  to  each  other,  whereas  two  or 
three  other  bodies  may  be  seen  which  resemble  Jupiter 
in  giving  a  steady  light,  and  also  in  changing  their 
place  from  night  to  night  among  the  fixed  stars.  I 
have  now  by  the  action  of  judgment  formed  in  my  mind 
the  general  notion  op  concept  of  fixed  stars,  by  bringing 
together  mentally  a  number  of  objects  which  agree ; 
while  from  several  other  objects  I  have  formed  the  gen- 
eral notion  of  planets.  Comparing  the  two  general 
notions  together,  I  find  that  they  do  not  possess  the 


14  INTRODUCrriOK. 

same  qualities  or  appearances,  which  I  state  in  the 
projwsition,  "  Planets  are  not  fixed  stars." 

The  expression  "  General  Notion  "  is  introduced  as  if  the 
learner  were  fully  actjuainted  with  it.  But  though  philosophers 
have,  for  more  tlian  two  tliouRund  years,  constantly  used  the  ex- 
pressions, general  notion,  idea,  conception,  concept,  etc.,  they 
have  never  succeeded  in  agreeing  exactly  as  to  the  meaning  of 
the  terms  One  class  of  philosophers,  called  Nominalists,  say 
that  it  is  all  a  matter  of  names,  and  that  when  we  join  together 
Jupiter,  Mars,  Saturn,  Venus,  etc.,  and  call  them  planets,  the 
common  name  is  the  bond  between  them  in  our  minds.  Others, 
railed  Realists,  have  asserted  that,  besides  these  particular 
planets,  there  is  really  something  which  combines  the  properties 
common  to  them  all,  without  any  of  the  differences  of  size, 
'olor,  or  motion  which  distinguish  them.  Every  one  allows  in 
the  present  day,  however,  that  nothing  can  physically  exist  cor- 
re8[K)nding  to  a  general  notion,  because  it  must  exist  here  or 
there,  of  tiiis  size  or  of  that  size,  and,  therefore,  it  would  be  on© 
particular  planet,  and  not  any  i>lanet  whatever.  The  Nominal- 
ists, too,  seetn  etjually  wronjj,  beaiuse  language,  to  be  of  any  use, 
must  denote  something,  and  must  correspond,  as  we  have  seen, 
to  acts  of  mind.  If  then  proper  names  raise  up  in  our  minds  the 
ima^res  of  particular  things,  like  Jupiter,  etc.,  general  names 
should  raise  up  gcmiral  notions. 

The  true  opinion  8e<>m8  to  be  that  of  the  philosophers  called 
Conceptualists,  who  say  that  the  general  notion  is  the  knowledge 
In  the  mind  of  the  common  properties  or  resemblances  of  the 
things  ombractnl  under  the  notion.  Thus,  the  notion  planet 
really  means  the  c<»nsciousnc88  in  anybody's  mind  that  there  are 
C4'rtain  heavenly  bodies  which  agree  in  giving  a  steady  light  and 
In  m»)ving  alK)ut  the  heavens  differently  from  the  fixwl  stars.  It 
Bhould  1k'  adde<l,  however,  that  there  are  many,  including  Sir  W. 
Hamilton,  who  would  be  counted  as  Nominalists,  and  who  yet 
hold  that  with  the  general  name  is  associated  a  consciousness  of 
th«'  rewrtiiblanc^!  existing  between  the  things  d«moted  by  it. 
B«'tween  tiiis  form  of  the  doctrine  and  conceptualism  it  is  not 
easy  to  draw  a  ])reriw'  distinction,  and  the  subject  is  of  too  d« 
Itttable  a  cliaracter  to  be  pursued  in  this  work. 


INTBODUCTION.  15 

(3)  Reasoning,  or  Discourse,  may  bt?  defined  as 
the  progress  of  the  miud  from  one  or  more  given  propo- 
sitions to  a  proposition  different  from  those  given. 
Those  propositions  from  which  we  argue  are  called 
Premises,  and  that  which  is  drawn  from  them  is  called 
the  Conclusion.  The  latter  is  said  to  follow,  to  he  con- 
cluded, inferred,  or  collected  from  them;  and  the 
premises  are  so  called  because  they  are  put  forward,  or 
at  the  beginning  (Latin  prcB^  before,  and  mitto,  I  sei^ 
or  put).  The  essence  of  the  process  consists  in  gather- 
ing the  truth  that  is  contained  in  the  premises  when 
joined  together,  and  carrying  it  with  us  into  the  con- 
clusion, where  it  is  embodied  in  a  new  proposition  or 
assertion.  We  extract  out  of  the  premises  all  the  in- 
formation which  is  useful  for  the  purpose  in  view — and 
this  is  the  whole  which  reasoning  accomplishes. 

It  will  appear  in  the  course  of  our  study  that  the  whole  of 
logic,  and  the  whole  of  any  science,  consists  in  so  arranging  the 
individual  things  we  meet  in  general  notions  or  classes,  and  in 
giving  them  appropriate  general  names  or  terms,  that  our 
knowledge  of  them  may  be  made  as  simple  and  general  as 
possible.  Every  general  notion  that  Js  properly  formed  admits 
of  the  statement  of  general  laws  or  truths  ;  thus  of  the  planets 
we  may  affirm  that  they  move  in  elliptic  orbits  round  the  sun 
from  west  to  east  ;  that  they  shine  with  the  reflected  light  of  the 
sun ;  and  so  on.  Of  the  fixed  stars  we  may  affirm  that  they 
shine  with  their  own  proper  light;  that  they  are  incomparably 
more  distant  than  the  planets;  and  so  on.  The  whole  of  reason- 
ing will  be  found  to  arise  from  this  faculty  of  judgment,  which 
enables  us  to  discover  and  affirm  that  a  large  number  of  objects 
have  similar  properties,  so  that  whatever  is  known  of  some  may 
be  inferred  and  asserted  of  others. 

It  is  in  the  application  of  such  knowledge  that  we  employ  the 
third  act  of  mind  called  discourse  or  reasoning,  by  which  from 
certain  judgments  we  are  enabled,  without  any  new  reference  to 


16  INTRODUCTION. 

the  real  objects,  to  form  a  new  judgment.  If  we  know  that  iron 
comss  under  the  general  notion  of  metal,  and  that  this  notion 
comes  under  the  still  wider  notion  of  element,  then,  without 
furt Her  examination  of  iron,  we  know  that  it  is  a  simple  unde- 
composable  substance  called  by  chemists  an  element.  Or  if 
from  one  source  of  information  we  learn  that  Neptune  is  a 
planet,  and  from  another  that  i)lanets  move  in  elliptic  orbits,  we 
can  join  tiiese  two  portions  of  knowledge  together  in  the  mind, 
BO  as  to  elicit  the  truth  that  Neptune  moves  in  an  elliptic  orbit. 

*  la.  Method  of  Treatment. 

Simple  apprehension  is  expressed  in  terms,  judgment 
in  propositions,  and  reasoning  in  syllogisms.  The  dis- 
cussion of  these  needs  to  be  supplemented  by  the 
exainination  of  fallacies  and  induction,  some  account  of 
logical  method,  and  a  view  of  recent  logical  theoriea 
Oui  chapters,  therefore,  will  be  as  follows  : 


1. 

Terms. 

2. 

I*i'Ofntsifions, 

3. 

Sf/f/of/isms. 

4. 

Fallacies. 

5. 

Int/iirtion. 

O. 

Mr  t  hod. 

1,    Rtrrjif  Logical  View8, 


LOGIC. 

CHAPTER    I. 
TERMS. 

In  the  treatment  of  Terms  we  shall  find  it  convenient 
to  consider:  (1)  The  Various  Kinds  of  Terms; 
(2)  The  Aiiibiffuity  of  Terms;  (3)  The  Two- 
fold Meaning  of  Terms,  in  Extension  and  In- 
tension;  (4)  The  Growth  of  Lnnf/fiaf/e ;  and 
(5)  The  Perfect  and  the  Imperfect  Know- 
ledf/e  of  Terms.  The  discussion  of  these  topics 
will  occupy  the  following  sections. 


SECTION    I, 

THE  VARIOUS    KINDS   OF  TERMS. 

1.   The  Meaning-  of  "Term"  Explained. 

It  has  been  explained  that  every  assertion  or  state- 
ment expresses  the  agreement  or  difference  of  two 
things,  or  of  two  general  notions.  In  putting  the 
assertion  or  statement  into  words,  we  must  accordingly 
have  words  suitable  for  drawing  the  attention  of  the 
mind  to  the  things  which  are  compared,  as  well  as 
words  indicating  the  result  of  the  comparison,  that  is 
to  say,  the  fact  whether  they  agree  or  differ.  The 
words  by  which  we  point  out  the  things  or  classes  of 
things  in  question  are  called  Terms,  and  the  words 
denoting  the  comparison  are  said  to  form  the  Copula. 


18  TERMS. 

Hence  a  complete  assertion  or  statement  consists  of 
two  terms  atid  a  copula,  and  when  thus  expressed  it 
forms  a  Proposition.  Thus  in  the  proposition  ''Dic- 
tionaries are  usot'ul  books,"  the  two  terms  are  diction- 
aries and  useful  books  ;  the  copula  is  the  verb  are,  and 
expresses  a  certain  agreement  of  the  class  dictionaries 
with  the  chiss  of  useful  books  consisting  in  the  fact 
that  the  class  of  dictionaries  forms  part  of  the  class  of 
useful  books.  In  this  case  each  term  consists  of  only 
one  or  two  words,  but  any  number  of  words  may  be 
required  to  describe  the  notions  or  classes  compared 
together.  In  the  proposition  "  the  angles  at  the  base 
of  an  isosceles  triangle  are  equal  to  each  other,"  the 
first  term  requires  nine  words  for  its  expression,  and 
the  second  term,  four  words  (equal  to  each  other);  and 
there  is  no  limit  to  the  number  of  words  which  may  \« 
employed  in  the  formation  of  a  term. 

A  Term  is  so  called  because  it  forms  one  end  (Latin,  terminiit) 
of  a  pro|;o8ition,  and  strictly  speaking  it  is  a  term  only  so  long  as 
it  stands  in  the  |)r<)position.  But  wo  commonly  speak  of  a  term 
or  a  name  meaning  any  noun,  substantive  or  adjective,  or  any 
combination  of  words  denoting  an  object  of  thought,  whether 
that  bo,  as  we  shall  shortly  see,  an  individual  thing,  a  group  of 
things,  a  quality  of  things,  or  a  group  of  qualities.  It  would  be 
imiK>sBible  to  define  a  name  or  term  better  than  has  been  done  by 
HoMh's  :  "  A  name  is  a  word  taken  at  pleasure  to  serve  for  a 
mark,  which  may  raise  in  our  mind  a  thought  like  to  some 
thought  which  wc;  had  l>ef()re,  and  which,  being  pronounced  to 
others,  may  be  to  them  a  sign  of  what  thought  the  Bi)eaker  had 
before  in  his  mind." 

2.  Catosroreiiiatic  and  Syiicategorematlc  Words. 

Though  every  term  or  name  consists  of  words,  it  la 
not  every  word  which  can  form  a  name  by  itaelf.     We 


YABIOUS  KIKDS   OF  TERMS.  19 

cannot  properly  say  "  Not  is  agreeable  "  or  "  Probably 
is  not  true;"  nothing  can  be  asserted  of  a  preposition, 
an  adverb,  and  certain  other  parts  of  speech,  except 
indeed  that  they  are  prepositions,  adverbs,  etc.  No 
pai't  of  speech  except  a  noun  substantive,  or  a  group  of 
words  used  as  a  noun  substantive,  can  form  the  subject 
or  first  term  of  a  proposition,  and  nothing  but  a  noun 
substantive,  an  adjective,  the  equivalent  of  an  adjec- 
tive, or  a  verb,  can  form  the  second  term  or  predicate 
of  a  proposition.  It  may  indeed  be  questioned  whether 
an  adjective  can  ever  form  a  term  alone ;  thus  in  "  Dic- 
tionaries are  useful,"  it  may  be  said  that  the  substan- 
tive tJmigs  or  hooks  is  understood  in  the  predicate, 
the  complete  sentence  being  "  Dictionaries  are  useful 
hooks  ;  "  but  as  this  is  a  disputed  point  we  will  assume 
that  words  are  divided  into  two  kinds  in  the  following 
manner :  — 

(1)  Words  which  stand,  or  appear  to  stand,  alone  as 
complete  terms,  namely  the  substantive  and  adjective, 
and  certain  parts  of  a  verb,  are  called  Categorematic 
words,  (from  the  Greek  word  KarT/yopt'w),  to  assert  or 
predicate. 

(2)  Those  parts  of  speech,  on  the  other  hand,  such 
as  prepositions,  adverbs,  conjunctions,  etc.,  which  can 
only  form  parts  of  names  or  terms,  are  called  Syncate- 
gorematic  words,  because  they  must  be  used  with  other 
words  in  order  to  compose  terms  (Greek  ovv,  with,  and 
KaTTjyopeu)).  Of  syncategorematic  words  we  need  not 
take  further  notice  except  so  far  as  they  form  part  of 
csategorematic  terms. 


20  TERMS. 

3.  Sini^iilar  Terms. 

Terms  are  distinguished  into  singular  or  individual, 
and  general  or  common  terms,  this  being  a  very  obvious 
division,  but  one  of  much  importance.  A  Singular 
term  is  one  wliich  can  denote  only  a  single  object,  so 
long  at  least  as  it  is  used  in  exactly  the  same  meaning ; 
thus  the  Emperor  of  the  French,  the  Atlantic  Ocean, 
St.  Paul's,  William  Shakspeare,  the  most  precious  of 
metals,  are  singular  terms.  All  proper  names  belong 
to  this  class ;  for  though  John  Jones  is  the  name 
of  many  men,  yet  it  is  used  not  as  meaning  any  of 
these  men,  but  some  single  man — it  has,  in  short,  a 
different  meaning  in  each  case,  just  as  London  in 
England,  has  no  connection  in  meaning  with  London 
HI  Canada. 

4.  General  Terms. 

General  terms  are  applicable  in  the  same  sense 
equally  to  any  one  of  an  indefinite  number  of  objects 
which  resemble  each  other  in  certain  qualities.  Thus 
vielal  is  a  general  name  because  it  may  be  applied 
indifferently  to  gold,  silver,  copper,  tin,  aluminium, 
or  any  of  about  fifty  known  substances.  It  is  not  the 
name  of  any  one  of  these  more  than  any  other,  and  it 
is  in  iiU'X  applied  to  any  substance  which  possesses 
metjillic  lustre,  which  cannot  be  decomposed,  and 
which  has  certain  other  (pialities  easily  recognized  by 
chemists.  Nor  is  the  number  of  substances  in  the 
class  restricted  ;  for  as  new  kinds  of  metal  are  from 
time  to  time  discovered  they  are  added  to  the  class. 
A  train,  while  Mars,  Jupiter,  Saturn,  etc.,  are  singular 


VABIOUS   KINDS   OF  TEEMS.  9\ 

ierms,  since  each  can  denote  only  a  single  planet,  ihe 
term  planet  is  a  general  one,  being  applicable  to  aa 
many  bodies  as  may  be  discovered  to  revolve  round  the 
sun  as  the  earth  does. 

5.  Collective  Terms.    • 

We  must  carefully  avoid  any  confusion  between 
general  and  collective  terms.  By  a  collective  term  we 
mean  the  name  of  a  number  of  things  when  all  joined 
together  as  one  whole  ;  like  the  soldiers  of  a  regimeiit, 
the  men  of  a  jury,  the  crew  of  a  vessel ;  thus  a  coll(  c- 
tive  term  is  the  name  of  all,  but  not  of  each.  A  genei-al 
term,  on  the  other  hand,  is  the  name  of  a  number  of 
things,  but  of  each  of  them  separately,  or,  to  use  t!ie 
technical  expression,  distributively.  Soldier,  jurymau, 
sailor,  are  the  general  names  which  may  belong  to  John 
Jones,  Thomas  Brown,  etc.,  but  Ave  cannot  say  that 
John  Jones  is  a  regiment,  Thomas  Brown  a  jury,  and 
so  on.  The  distinction  is  exceedingly  obvious  wiien  thus 
pointed  out,  but  it  may  present  itself  in  more  obscure 
forms,  and  is  then  likely  to  produce  erroneous  reason- 
ing. It  is  easy  to  see  that  we  must  not  divide  terms 
into  those  which  are  general  and  those  which  are  col- 
lective, because  it  will  often  happen  that  the  same  term 
is  both  general  and  collective,  according  as  it  is  regard- 
ed. Thus,  library  is  collective  as  regards  the  books  in 
it,  but  is  general  as  regards  the  great  number  of  differ- 
ent libraries,  private  or  public,  which  exist. 

Regiment  is  a  collective  term  as  regards  the  soldiers  wliish 
compose  it,  but  greneral  a^  regards  the  hundred  different  re^- 
ments.   the   Coldstream   Guards,   the    Highland    regiment,    the 


22  TERMS. 

Weleh  Fusiliers,  and  the  rest,  which  compose  the  British  stand- 
ing army.  Army,  ivgaln,  is  a  collective  whole,  as  being  composed 
of  a  number  of  rej^ments  organized  together.  Year  is  collective 
as  regards  tlie  months,  weeks,  or  days  of  which  it  consists,  but  is 
general  as  being  the  name  either  of  1869  or  1870,  or  any  period 
marked  by  a  revolution  of  the  earth  round  the  son. 

We  have  not  always  in  the  English  language  suflScient  means 
of  distinguishing  conveniently  between  tlie  general  and  collec- 
tive use  of  terms.  In  Latin  this  distinctive  use  was  exactly 
expressed  by  omnea,  meaning  all  distributively,  and  cuncti 
meaning  all  taken  together,  a  contracted  form  of  conjuncti 
(joined  together).  In  Englisli  cUl  men  may  mean  any  vKin  or  all 
men  together.  Even  the  more  exact  word  every  is  sometimes 
misused,  as  in  the  old  proverb,  "  Every  little  makes  a  mickle," 
where  it  is  obvious  that  every  little  portion  cannot  by  itself  make 
much,  but  only  when  joined  to  other  little  portions. 

6.  Concrete  and  Abstract  Terms. 

An  important  distinction  between  terras  is  that  of 
concrete  terms  and  abstract  terms;  and  it  cannot  oe 
better  described  than  in  tlie  words  of  Mr.  Mill,  by  say- 
ing that  a  concrete  name  is  the  name  of  a  thing,  the 
abstract  name  i.s  the  name  of  a  quality,  attribute,  or 
circumst4ince  of  a  thing.  Thus  red  house  is  the  name 
of  a  physically-existing  thing,  and  is  concrete;  redness 
is  the  name  of  one  quality  of  the  house,  and  is  abstract. 
The  word  abstract  means  drawn  from  (Latin,  abstrac- 
tu8,  from  ahslrahere,  to  draw  away  from),  and  indi- 
cates that  the  quality  redness  is  thought  of  in  the  mind 
a])art  from  all  the  other  qualities  which  belong  to  the 
red  house,  or  other  red  object.  But  though  we  can 
think  of  a  quality  by  itself,  we  cannot  suppose  that  the 
quality  can  exist  physically  apart  from  the  matter  in 
which  it  is  raauifcst  to  us.     Redness  means  either  a 


TABIOUS  KINDS  OF  TERMS.  38 

notion  in  the  mind,  or  it  means  that  in  red  objecta 
which  excitee  the  notion. 

The  learner  should  carefully  observe  that  adjectives  are  con- 
crete, not  abstract.  If  we  say  that  a  lx)ok  is  useful,  it  is  to  the 
book  we  apply  the  adjective  usefiU,  and  usefulness  is  the  abstract 
noun  which  denotes  the  quality  ;  similarly,  the  adjectives  equal, 
grateful,  reverent,  rational,  are  the  names  of  thinjrs,  and  the 
corresponding  abstract  nouns  are  equality,  gratitude,  reverence, 
rationality. 

It  is  a  good  exercise  to  try  to  discover  pairs  of  correspond- 
ing concrete  and  abstract  names;  thus  animal  has  animality; 
miser,  miserliness  ;  old,  agedness,  or  old  age  ;  substance,  sub- 
stantiality ;  soap,  Boapiness ;  shrub,  shrubbiness  ;  and  so  on.  But 
it  by  no  means  follows  that  an  abstract  word  exists  for  each  con- 
crete ;  table  hardly  has  an  abstract  tabularity  ;  and  though  ink 
has  inkiness,  we  should  not  find  the  abstract  of  pen.  It  is  by 
the  accidents  of  the  history  of  language  that  we  do  or  do  not 
possess  abstract  names ;  and  there  is  a  constant  tendency  to 
invent  new  abstract  words  in  the  progress  of  time  and  science. 

Unfortunately  concrete  and  abstract  names  are  frequently 
confused,  and  it  is  by  no  means  always  easy  to  distinguish  the 
meanings.  Thus  relation  properly  is  the  abstract  name  for  the 
position  of  two  people  or  things  to  each  other,  and  those  people 
are  properly  called  relatives  (Latin,  relativus,  one  who  is  related). 
But  we  constantly  speak  now  of  relations,  meaning  the  persons 
themselves ;  and  when  we  want  to  indicate  the  abstract  relation 
they  have  to  each  other  we  have  to  invent  a  new  abstract  name 
relationship.  Nation  has  long  been  a  concrete  term,  though  from 
its  form  it  was  probably  abstract  at  first ;  but  so  far  does  the 
abuse  of  language  now  go,  especially  in  newspaper  writing,  that 
we  hear  of  a  nationality  meaning  a  nation,  although  of  course  if 
nation  is  the  concrete,  nationality  ought  to  be  the  abstract, 
meaning  the  quality  of  being  a  nation.  Similarly,  action,  inten- 
tion, extension,  conception,  and  a  multitude  of  other  properly 
abstract  names,  are  used  confusedly  for  the  corresponding  con- 
crete, namely,  act,  intent,  extent,  concept,  etc.  Production  it 
properly  the  condition  or  state  of  a  person  who  is  producing  or 


S4  TBBUS. 

drawing  something  forth  ;  but  it  has  now  become  confused  wit! 
that  which  is  produced,  bo  that  we  constantly  talk  of  the  produc- 
tions of  a  country,  meaning  the  products.  The  logical  terms, 
Proposition,  Deduction,  Induction  Syllogism,  are  all  properly 
abstract  words,  but  are  used  concretely  for  a  Proposition,  a  De- 
duction, an  Induction,  a  Syllogism  ;  and  it  must  be  allowed  that 
logicians  are  nearly  as  bad  as  other  people  in  confusing  abstract 
and  concrete  terms.  Much  injury  is  done  to  language  by  this 
abuse. 

7.  Positive  and  Negative  Terms. 

Another  very  obvious  division  of  terms  is  between 
those  which  are  positive,  and  those  which  are  negative. 
The  difference  is  usually  described  by  saying  that  posi- 
tive terms  signify  the  existence  or  possession  of  a 
quality,  as  in  grateful,  metallic,  organic,  etc.,  while 
the  corre.sjwnding  negatives  signify  the  absence  of  the 
same  qualities  as  in  ungrateful,  non-metallic,  inorganic. 
The  negative  terms  may  be  adjectives  as  above,  or  sub- 
stantives, concrete  or  abstract ;  thns  ingratitude,  in- 
equality, inconvenience,  are  abstract  negative  terms; 
and  individuals,  uncquals,  etc.,  arc  concrete  negatives. 
We  usually  consider  as  negative  terms  any  which  have 
a  negative  prefix  such  as  not,  non,  un,  in,  etc. ;  but 
there  are  a  great  many  terms  which  serve  as  negatives 
without  possessing  any  mark  of  their  negative  charac- 
ter. Darkness  is  the  negative  of  light  or  lightness, 
since  it  means  the  absence  of  light ;  compound  is  the 
negative  of  element,  since  we  should  give  the  name  of 
compound  to  whatever  can  bo  decomposed,  and  element 
is  what  cannot  Ix;  decomposed  ;  theoretically  speaking 
every  term  has  its  corresponding  negative,  but  it  by  na 
means  follows  that  language  furnishes  the  term  ready- 


VABIOUS  KINDS  OF  TERMS.  85 

made.  Thus  table  has  the  corresponding  adjective  tab- 
ular, but  there  is  no  similar  negative  untabular ;  one 
man  may  be  called  a  bookworm,  but  there  is  no  nega- 
tive for  those  who  are  not  bookworms,  because  no  need 
of  the  expression  has  been  felt.  A  constant  process  of 
invention  of  new  negative  terms  goes  on  more  rapidly 
perhaps  than  is  desirable,  for  when  an  idea  is  not 
often  referred  to  it  is  better  to  express  it  by  a  phrase 
than  add  to  the  length  of  the  dictionary  by  a  new- 
created  word. 

It  would  peem  that  in  many  cases  a  negative  term  implies  the 
presence  of  some  distinct  quality  or  fact.  Thus  inconvenience 
doubtless  implies  the  absence  of  convenience,  but  also  the  pres 
ence  of  positive  trouble  or  pain  occasioned  thereby.  Unhappi 
ness  is  a  negative  term,  but  precisely  tlie  same  notion  is 
expressed  by  the  positive  term  misery.  The  negrative  of  healthy 
is  unhealthy,  but  the  positive  term  sickly  serves  equally  well. 
It  thus  appears  to  be  more  a  matter  of  accident  than  anything 
else  whether  a  positive  or  negative  term  is  used  to  express  any 
particular  notion.  All  that  we  can  really  say  is  that  every  posi 
tive  term  necessarily  implies  the  existence  of  a  corresponding 
negative  term,  which  may  be  the  name  of  all  those  things  to 
which  the  positive  name  cannot  be  applied.  Whether  this  term 
has  been  invented  or  not  is  an  accident  of  language  ;  its  existence 
may  be  assumed  in  logic. 

The  reader  may  be  cautioned  against  supposing  that  every 
term  appearing  to  be  of  a  negative  character  on  account  of 
possessing  a  negative  prefix  is  really  so.  The  participle  unloosed 
certainly  appears  to  be  the  negative  of  loosed  ;  but  the  two  words 
mean  exactly  the  same  thing,  the  prefix  rin  not  being  really  the 
negative  ;  invaluable,  again,  means  not  what  is  devoid  of  value, 
but  what  is  so  valuable  that  the  value  cannot  be  measured ;  and 
d  shameless  action  can  equally  be  called  by  the  positive 
term,  a  shameful  action.  Other  instances  might  no  doubt  be 
found. 

Great  care  should  be  taken  to  avoid  confusing  terms  which 


26  TEBMS. 

express  the  presence  or  absence  of  a  quality  with  those  whici 
describe  its  degree.  Less  is  not  tin-  uegative  of  greater  because 
there  is  a  third  alternative,  equal.  The  true  negative  of  greater 
is  not-greater,  and  thi«  is  equivalent  to  either  equal  or  less.  Sf^  it 
may  be  said  that  dimgreeaUe  is  not  the  simple  negative  of  agree- 
able,  b..'cau8o  there  may  be  things  which  are  neither  one  nor  the 
other,  but  are  indifferent  to  us.  It  would  not  be  easy  to  say  ot[» 
hand  whether  every  action  which  is  not  honest  is  dishonest,  oj 
whether  there  may  not  be  actions  of  an  intermediate  character. 
The  rule  is  that  wherever  the  question  is  one  of  degree  or  quan 
tity  a  medium  is  possible,  and  the  subject  belongs  rather  to  the 
science  of  quantity  than  to  simple  logic  ;  where  the  question  is 
one  of  the  presence  or  absence  of  a  quality,  there  cannot  be  more 
than  two  alternatives,  according  to  one  of  the  Primary  Laws  of 
Thought,  which  we  will  consider  in  Chap.  Ill,  Sec.  I.  In  the 
case  of  quantity  we  may  call  tlie  extreme  terms  opposites ;  thus 
less  is  the  opposite  of  greater,  disagreeable  of  agreeable ;  in  the 
case  of  mere  negation  we  may  call  the  terms  negatives  or  con- 
tradictories, and  it  is  really  indifferent  in  a  logical  point  ox 
view  wliich  of  a  pair  of  contradictory  terms  we  regard  as  the 
positive  and  which  as  the  negative.  Each  is  the  negative  of  the 
other. 

8.  Privative  Terms. 

Logicians  have  distinguished  from  simple  negative 
terms  a  class  of  terms  called  privative,  such  as  blind, 
dead,  etc.  Such  terms  express  that  a  thing  has  been 
ie;;nm/ of  a  quality  which  it  before  possessed,  or  was 
capable  of  possessing,  or  usually  does  possess.  A  man 
may  be  born  blind,  so  that  he  never  did  see,  but  he 
possesses  the  organs  wliich  would  have  enabled  him  to 
see  except  for  some  accident.  A  stone  or  a  tree  could 
not  have  had  the  faculty  of  seeing  under  any  circum- 
sUmces.  No  mineral  substance  can  ])roperly  be  said  to 
die  or  to  be  dead,  because  it  was  incapable  of  life  ;  but 


VARIOUS  KINDS  OF  TERMS.  27 

it  may  be  called  uncrystallized  because  it  might  hav« 
been  in  the  form  of  a  crystal.  Hence  we  apply  a 
privative  term  to  anything  which  has  not  a  quality 
which  it  was  capable  of  having;  we  apply  a  negative 
term  to  anything  which  has  not  and  could  not  have  the 
quality.  It  is  doubtful  however  whether  this  distinc- 
tion can  be  properly  carried  out,  and  it  is  not  of  very 
much  importance. 

9.  Relative  and  Absolute  Terms. 

It  is  further  usual  to  divide  terms  according  as  they 
are  relative  or  absolute,  that  is,  non-relative.  The 
adjective  absolute  means  whatever  is  "  loosed  from  con- 
nection with  anything  else "  (Latin  ah,  from,  and 
solutus,  loosed) ;  whereas  relative  means  that  which  is 
carried  in  thought,  at  least,  into  connection  with  some- 
thing else.  Hence  a  relative  term  denotes  an  object 
which  cannot  be  thought  of  without  reference  to  some 
other  object,  or  as  part  of  a  larger  whole,  A  father 
cannot  be  thought  of  but  in  relation  to  a  child,  a 
monarch  in  relation  to  a  subject,  a  shepherd  in  relation 
to  a  flock;  thus  father,  monarch,  and  shepherd  are 
relative  terms,  while  child,  subject,  and  flock  are  the 
correlatives  (Latin  con,  with,  and  relativus),  or  those 
objects  which  are  necessarily  joined  in  thought  with 
the  original  objects.  The  very  meaning,  in  fact,  of 
father  is  that  he  has  a  child,  of  monarch  that  he  has 
subjects,  and  of  shepherd  that  he  has  a  flock.  As 
examples  of  terms  which  have  no  apparent  relation  to 
anything  else,  I  may  mention  water,  gas,  tree.  There 
does  not  seem  to  me  to  be  anything  so  habitually  asso- 
ciated with  water  that  we  must  think  of  it  as  part  of 


S8  TERMS. 

the  same  idea,  and  gas,  tree,  and  a  multitude  of  othei 
terms  also  denote  objects  wliich  have  no  remarkable  or 
permanent  relations  such  as  would  entitle  the  terras  to 
be  called  relatives.  They  may  therefore  be  considered 
absolute  or  non-relative  terms. 

The  fact,  however,  is  that  everything  must  really  have  rela- 
tions to  something  else,  the  water  to  the  elements  of  which  it  is 
comix)sed,  the  yas  to  the  coal  from  which  it  is  manufactured, 
the  tree  to  the  soil  in  wliich  it  is  rooted.  By  the  very  laws  of 
thought,  again,  no  thing  or  class  of  things  can  be  thought  of  but 
by  separatini^  them  from  other  existing  things  from  which  they 
differ.  I  cannot  use  the  tenii  mortal  without  at  once  separating 
all  existing  or  conceivable  tilings  into  the  two  groups  mortal  and 
immorUil ;  motal,  element,  organic  substance,  and  every  other 
term  that  could  be  mentiomid,  Avould  necessarily  imply  the 
existence  of  a  correlative  negative  term,  non  metallic,  compound, 
inorganic  substance,  and  in  this  respect  therefore  every  term  is 
undoubtedly  relative.  Logicians,  however,  have  been  content  to 
consider  as  relativt;  terms  those  only  which  imply  some  peculiar 
and  striking  kind  of  relation  arising  from  position  in  time  or 
Bpac<',  from  connection  of  cause  and  effect,  etc.;  and  it  is  in  this 
8i*eciul  sense  therefore  the  student  must  use  the  distinction. 

10.  Siiininary. 

The  most  important  varieties  of  terms  having  been 
explained,  it  is  desirable  that  the  learner  should  acquire 
a  complete  familiarity  with  them  by  employing  the  exer- 
cises at  the  end  of  the  book.  The  learner  is  to  deter 
mine  concerning  each  of  the  terms  there  given:  — 

1.  mother  it  is  a  ratef/oreinatlc  or  a  ny ncateff ore- 

mat  ir,  ivord. 

2.  Wlielhrr  it  in  a  f/eneral  or  a  ninffulnr  tertn. 

3.  If'/irthrr  it  i.s  collrctive  or  distributive. 

4.  WlieUtMr  it  is  concrete  or  abstract. 


VARIOUS  KINDS  OF  TERMS.  89 

S,  JFhether  it  is  positive,  or  negative^  or  priva- 
tive, 
€,   Whether  it  is  relative  or  absolute. 

It  will  be  fully  pointed  out  in  the  next  section  that  most 
r«rms  have  more  than  one  meaninjf ;  and  as  the  one  meaning 
may  be  general  and  the  other  singular,  the  one  concrete  and  the 
other  abstract,  and  so  on,  it  is  absolutely  necessary  that  the 
learner  should  first  of  all  choose  one  precise  meaning  of  the 
term  which  he  is  examining.  And  in  answering  the  questions 
proposed  it  is  desirable  he  should  specify  the  way  in  which  he 
regards  it.  Taking  the  word  sovereign,  we  may  first  select  the 
meaning  in  which  it  is  equivalent  to  monarch  ;  this  is  a  general 
term  in  so  far  as  it  is  the  name  of  any  one  of  many  monarclis 
living  or  dead,  but  it  is  singular  as  regards  the  inhabitants,  of  any 
one  country.  It  is  clearly  categorematic,  concrete,  and  positive 
and  obviously  relative  to  the  subjects  of  the  monarch. 

Read  Mr.  Mill's  chapter  on  Names,  System  of  Logic,  Book  I, 
chap.  2. 

In  this  section  on  "  Various  Kinds  of  TerniSf" 
we  have  considered: — 

1.  Tlie  Meaning  of  "  Term,'* 

2.  Categoretnutic and  Syncategoreniatic  WordA 

3.  Singular  Terms, 
4-.  General  Terms. 

5.  Collective  Terms. 

6.  Concrete  and  Abstract   Terms. 

7.  Positive  and  Negative  Terms. 

8.  Privative  Terms. 

9.  Relative  and  Absolute  Terms, 


30  TE&HS. 

SECTION   n. 

THE  AMBIGUITY   OF  TERMS. 

1.  Importance  of  Avoiding  Ambiguity. 

There  is  no  part  of  Logic  which  is  more  really  usefui 
than  that  which  treats  of  the  ambiguity  of  terms,  that 
is,  of  the  uncertainty  and  variety  of  meanings  belong- 
ing to  words.  Nothing  indeed  can  be  of  more  impor- 
tance to  the  attainment  of  correct  habits  of  thinking 
and  reasoning  than  a  thorough  acquaintance  with  the 
great  imperfections  of  language.  Comparatively  few 
terms  have  one  single  clear  meaning  and  one  meaning 
only,  and  whenever  two  or  more  meanings  are  uncon- 
sciously confused  together,  we  inevitably  commit  a 
logical  fallacy.  If,  for  instance,  a  person  should  argue 
that  ''punishment  is  an  evil,"  and  according  to  the 
principles  of  morality  "  no  evil  is  to  be  allowea  even  with 
the  purpose  of  doing  good,"  we  might  not  at  the  first 
moment  see  how  to  avoid  the  conclusion  that  "  no  pun- 
ishments should  be  allowed,"  because  they  cause  evil. 
A  little  reflection  will  show  that  the  word  evil  is  here 
used  in  two  totally  different  senses ;  in  the  first  case  it 
means  physical  evil  or  pain ;  in  the  second,  moral  evil ; 
and  because  moral  evil  is  never  to  be  committed,  it  does 
not  follow  that  physical  evils  are  never  to  be  inflicted, 
for  they  are  often  the  very  means  of  preventing  moral 
aril. 

Another  very  plausible  fallacy  which  has  often  been  put 
forth  in  various  forms  is  as  follows:  "A  thoroujjbly  lienevolent 
man  cannot  posBibly  rofuse  to  relieve  the  y)Oor,  and  since  a  per 
•on  wlio  cannot  {xjssibly  act  otherwise  than  he  does  can  claim  n« 


THE  AMBIGUITY  OF  TEBMS.  81 

merit  for  his  actions,  it  follows  that  a  thoroughly  benevolent  man 
can  claim  no  merit  for  his  actions."  According  to  tliis  kind  o/ 
argument  a  man  would  have  less  merit  in  projwrtion  as  he  waa 
more  virtuous,  so  as  to  feel  greater  and  greater  diflSculty  in  act- 
ing wrongly.  That  the  conclusion  is  fallacious  every  one  must 
feel  certain  ;  but  the  cause  of  the  fallacy  can  only  be  detected  by 
observing  that  the  words  cannot  possibly  have  a  double  meaning, 
in  the  first  case  referring  to  the  influence  of  moral  motives  or 
good  character,  and  in  the  second  to  circumstances  entirely  be- 
yond a  person's  control ;  as,  for  instance,  the  compulsion  of  the 
laws,  the  want  of  money,  the  absence  of  personal  liberty.  The 
more  a  person  studies  the  subtle  variations  in  the  meaning  of 
common  words,  the  more  he  will  be  convinced  of  the  dangerous 
nature  of  the  tools  he  has  to  use  in  all  communications  and  argu- 
ments. Hence  the  learner  should  give  much  attention  to  the 
contents  of  this  section. 

2.  Uni vocal  and  Equivocal  Terms. 

Terms  are  said  to  be  univocal  when  they  can  suggest 
to  the  mind  no  more  than  one  single  definite  meaning. 
They  are  called  equivocal  or  ambiguous  when  they  have 
two  or  more  different  meanings.  It  will  be  observed, 
however,  that  a  term  is  not  equivocal  because  it  can  be 
applied  to  many  objects  when  it  is  applied  in  the  same 
sense  or  meaning  to  those  different  objects.  Thus 
cathedral  is  the  name  of  St.  Paul's,  the  York  Minster, 
and  the  principal  churches  of  Salisbury,  "Wells,  Lincoln 
and  a  number  of  other  cities,  but  it  is  not  ambiguous, 
because  all  these  are  only  various  instances  of  the  same 
meaning  ;  they  are  all  objects  of  the  same  descnj)tion 
or  kind.  The  word  cathedral  is  probably  univocal  or 
of  one  logical  meaning  only.  The  word  church,  on  the 
other  hand,  is  equivocal,  because  it  sometimes  meana 
the  building  in  which  religious  worship  is  performed, 


82  TBBM8. 

so'netimes  the  body  of  persons  who  belong  to  one  sect 
or  }>ersiKirfion,  and  assemble  in  churches.  Sometimes 
alh<o  the  church  means  the  body  of  the  clergy  as  distin- 
guished from  the  laity ;  hence  there  is  u  clear  differ- 
ence in  the  sense  or  meaning  with  which  the  word  is 
used  at  different  times. 

Instances  of  univocal  terms  are  to  be  found  chiefly  in  technical 
an<l  scientific  language.  Steam  engine,  gasometer,  railway  train, 
permanent  way,  and  multitudes  of  such  technical  names  denot- 
in|^  distinct  common  objects,  are  sufficiently  univocal  In  com- 
mon life  the  names  penny,  mantelpiece,  teacup,  bread  and  butter, 
have  a  sufficiently  definite  and  single  meaning.  So  also  in  chem- 
ist rj',  oxygen,  hydrogen,  sulphate  of  copper,  alumina,  lithia,  and 
thi'USiinds  of  other  terms,  are  very  precise,  the  words  themselvea 
having  often  been  invented  in  very  recent  years,  and  the  mean- 
ings exactly  fixed  and  maintained  invarialile.  Every  science 
has,  or  ouglit  to  have,  a  series  of  terms  equally  precise  and  cer- 
tain in  meaning.  The  names  of  individual  objects,  buildings, 
ev.-nts,  or  persons,  again,  are  usually  quite  certain  and  clear 
fts  Julius  Caesar,  William  the  Conqueror,  the  first  Napoleon. 
Saint  Peter's,  Westmioster  Abbey,  the  Great  Exhibition  of  1851 
an  1  so  on. 

But  however  numerous  may  be  the  univocal  terms  which  can 
bt!  adduced,  still  the  e(piivr>cal  terms  are  astonishingly  common. 
Tliey  include  most  of  the  nouns  and  adjectives  which  are  in 
habitual  use  in  the  ordinary  intercourse  of  life.  They  are  called 
ambiguous  from  the  Latin  verb  ambigo,  to  wander,  hesitate,  or 
bo  in  doubt ;  or  again  hamonymo'is,  from  the  Oreek  ofior,  like, 
and  oioua,  name.  Whenever  a  ]>er8on  uses  equivocal  words  in 
Buch  a  way  as  to  confuse  the  different  meanings  and  fall  into 
error,  he  may  be  said  to  commit  the  fallacy  of  Equivocation  in 
the  logical  meaning  of  the  name  (see  Cliapter  IV)  ;  but  in  com- 
mon life  a  person  is  not  said  to  equivocate  unless  he  uses  wordi 
cons'iouHly  and  deceitfully  in  a  manner  calculated  to  producer 
ooufunou  of  the  true  and  apparent  meanings. 


THE  AMBIGUITY    OF  TERMS.  B$ 

3.  Kinds  and  Causes  of  Ambiguity. 

Following  Dr.  Watts  in  classifying  equivocal  words, 
ire  may  distinguish  three  classes  according  as  they  are— 

1.  Equivocal  in  sound  only. 

2.  Equivocal  in  spelling  only. 

3.  Equivocal  in  both  sound  and  spelling. 

The  first  two  classes  are  comparatively  speaking  of  very 
slight  importance,  and  do  not  often  give  rise  to  serious 
error.  They  produce  what  we  should  call  trivial  mis- 
takes. Thus  we  may  confuse,  when  spoken  only,  the 
words  right,  wright,  and  rite  (ceremony);  also  the  words 
rein,  rain  and  reign,  might  and  mite,  etc.  Owing 
partly  to  defects  of  pronunciation  mistakes  are  not 
unknown  between  the  four  words  air,  hair,  har.e  and 
heir. 

Words  equivocal  in  spelling  but  not  in  sound  are 
such  as  tear  (a  drop),  and  tear  pronounced  tare,  mean- 
ing a  rent  in  cloth ;  or  lead,  the  metal,  and  lead,  as  in 
following  the  lead  of  another  person.  As  little  more 
than  momentary  misapprehension,  however,  can  arise 
from  such  resemblauce  of  words,  we  shall  pass  at  once 
to  the  class  of  words  equivocal  both  in  sound  and  spell- 
ing. These  I  shall  separate  into  three  groups  accord 
ing  as  the  equivocation  arises — 

1.  From  the  accidental  confusion  of  different  words. 

2.  From  the  transfer  of  meaning  by  the  association 

of  ideas. 

3.  From  the  logical  transfer  of  meaning  to  analogous 

objects. 


34  TERICS. 

(1)  Under  the  first  class  we  place  a  certain  numbei 
of  curious  but  hardly  important  cases  in  which  ambi< 
guity  lias  arisen  from  tiie  confusion  of  entirely  different 
•vords,  derived  from  different  languages  or  from  differ- 
ent roots  of  the  same  language,  but  which  have  in  the 
course  of  time  assumed  the  same  sound  and  spelUng. 
Thus  the  word  mean  denotes  either  that  which  is 
medium  or  mediocre,  from  the  French  moyen  and  the 
Latin  medius,  connected  with  the  Anglo-Saxon  mid, 
or  middle;  or  it  denotes  what  is  low-minded  and  base, 
being  then  derived  from  the  Anglo-Saxon  Gemoene, 
which  means  *•  that  belonging  to  the  moene  or  many," 
whatever  in  short  is  vulgar.  The  verb  to  mecw  can 
hardly  be  confused  with  the  adjective  mean,  but  it 
comes  from  a  third  distinct  root,  probably  connected 
with  the  Sanscrit  verb,  to  think. 

As  other  instances  of  this  casual  ambiguity,  I  may  mention 
rent,  a  money  payment,  from  the  French  reitte  (rendre,  to  return), 
or  a  toar,  the  result  of  the  action  of  rending,  this  word  being  of 
Anglo-Saxon  origin  and  one  of  the  numerous  class  beginning  in 
r  or  wr,  which  imitate  more  or  less  perfectly  the  sound  of  the 
action  which  they  denote.  Pound,  from  the  Latin  pondiis,  a 
weijfht,  is  confused  with  pound,  in  tlie  sense  of  a  village  pinfold 
for  cattle,  derivi-d  from  the  Saxon  pyndnn,  to  pen  up.  Fell,  » 
mountain,  is  a  perfectly  distinct  word  from  feV,  a  skin  or  hidd; 
and  puhf,  a  throb  or  boating,  and  piihe,  peas,  Ijeans,  or  potage, 
though  l)oth  derived  from  the  Oreek  or  Latin,  are  probably  quite 
anconn«'cte<i  words.  It  is  curious  that  gin,  in  the  meaning  of 
trap  or  machine,  is  a  contracted  form  o^  engine,  and  when  denote 
ing  the  spirituous  licjuor  is  a  corruption  of  Oeneva,  the  place 
where  the  spirit  was  first  made. 

Certain  important  cases  of  confusion  have  been  detected  in 
grammar,  as  between  the  numeral  one,  derived  from  an  Aryan 
root,  through  the  Latin  unuH,  and  the  indeterminate  pronoun, 
oru  (aa  in  "  one  ought  to  do  one'a  duty  "),  which  is  really  a  corrupt 


THE   AMBIGUITY   OF  TERMS.  M 

form  of  the  French  word  homme  or  man.     The  GennanB  to  tht 
present  day  use  man  in  this  sense,  as  in  man  sagt,  i.  e.  one  b&jb. 

(2)  By  far  the  largest  part  of  equivocal  words  have 
become  so  by  a  transfer  of  the  meaning  from  the  thing 
originally  denoted  by  the  word  to  some  other  thing 
habitually  connected  with  it  so  as  to  become  closely 
associated  in  thought.  Thus,  in  Parliamentary  Ian 
guage,  the  House  means  either  the  chamber  in  whicl 
the  members  meet,  or  it  means  the  body  of  members 
who  happen  to  be  assembled  in  it  at  any  time.  Simi- 
larly, the  word  church  originally  denoted  the  building 
(KvpiaKov,  the  Lord's  House)  in  which  any  religious 
worshippers  assemble,  but  it  has  thence  derived  a 
variety  of  meanings  ;  it  may  mean  a  particular  body  of 
worshippers  accustomed  to  assemble  in  any  one  place, 
in  which  sense  it  is  used  in  Acts  xiv.  23 ;  or  it  meana 
any  body  of  persons  holding  the  same  opinions  and 
connected  in  one  organization,  as  in  the  Anglican,  or 
Greek,  or  Roman  Catholic  Church  ;  it  is  also  sometimes 
used  so  as  to  include  the  laity  as  well  as  the  clergy; 
but  more  generally  perhaps  the  clergy  and  religious 
authorities  of  any  sect  or  country  are  so  strongly  asso- 
ciated with  the  act  of  worship  as  to  be  often  called  the 
church  par  excellence.  It  is  quite  evident,  moreover, 
that  the  word  entirely  differs  in  meaning  according  as 
it  is  used  by  a  member  of  the  Anglican,  Greek,  Eoman 
Catholic,  Scotch  Presbyterian,  or  any  other  existing 
church. 

The  word  foot  has  suffered  several  curious  but  very  evident 
transfers  of  meaning.  Originally  it  denoted  the  foot  of  a  man 
or  an  animal,  and  is  probably  connected  in  a  remote  manner  with 
the  Latin  pes,  pedis,  and  the  Greek  ttovc,  no66c ;  but  since  th« 


36  TEBM8. 

length  of  the  foot  is  naturally  employed  as  a  rude  measure  oi 
length,  it  came  to  be  applied  to  a  fixed  measure  of  length  ;  and 
as  the  foot  is  at  the  Ixjttom  of  the  body  the  name  was  extended 
by  analogy  to  the  foot  of  a  mountain,  or  the  feet  of  a  table ;  by  a 
further  extension,  any  position,  plan,  reason,  or  argument  on 
which  we  place  ourselves  and  rely,  is  called  the  foot  or  footing. 
The  same  word  also  denotes  soldiers  who  fight  ujwn  their  feet, 
or  infantry,  and  the  measured  part  of  a  verse  having  a  definite 
lengtli.  That  these  veiy  diflerent  meanings  are  naturally  con- 
nected  with  the  original  meaning  is  evident  from  the  fact  that 
the  Latin  and  Greek  words  for  foot  are  subject  to  exactly  similar 
series  of  ambiguities. 

It  would  be  a  long  task  to  trace  out  completely  the  various 
and  often  contradictory  meanings  of  tlie  word  fellow.  Originally 
a  fellow  was  what /'^^ow*  another,  that  is  a  companion;  thus  it 
came  to  mean  the  other  of  a  pair,  as  one  shoe  is  the  fellow  of  the 
other,  or  simply  an  ecjual,  as  when  we  say  that  Shakespeare 
"  hath  not  a  fellow."  From  the  simple  meaning  of  companion 
again  it  comes  to  denote  vaguely  a  person,  ns  in  the  question 
"  What  fellow  is  that?  "  but  then  there  is  a  curious  confusion  of 
depreciatory  and  endearing  power  in  the  word  ;  when  a  man  is 
called  a  mere  fellow,  or  simply  a  fellow  in  a  particular  tone  of 
voice,  the  name  is  one  of  severe  contempt;  alter  the  tone  of 
voice  of  the  connected  words  in  the  least  degree,  and  it  becomes 
one  of  the  most  sweet  and  endearing  appellations,  as  when  we 
speak  of  a  dear  or  good  fellow.  We  may  still  add  the  technical 
meanings  of  the  name  as  applied  in  the  case  of  a  Fellow  of  a 
College,  or  of  a  learned  society. 

Another  good  instance  of  the  gro^vth  of  a  numlxjr  of  different 
meanings  from  a  single  root  is  found  in  the  word  post.  Origi- 
nally a  post  was  something  powYerf,  or  placet!  fimily  in  the  ground 
8'ich  ua  an  upriglit  piece  of  wood  or  stone  :  such  meaning  stiD 
remains  in  the  cases  of  a  lamp  post,  a  gate  powt,  signal  post,  eta 
As  a  p!)«t  would  often  be  us<^  to  mark  a  fixed  spot  of  ground,  as 
in  a  mile-post,  it  came  to  mean  the  fixed  or  appointed  place 
wliere  tlie  fjost  was  placed,  as  in  a  military  post,  the  post  of  dan- 
ger or  honor,  etc.  Tlie  fixed  places  where  horses  were  kept  in 
readiness  to  facilitate  rapid  travelling  during  the  timee  of  the 


THE  AMBIGUITY    OF  TEEMS.  87 

Roman  empire  were  thus  called  posts,  and  thence  the  whcl4 
system  of  arrangement  for  the  conveyance  of  persons  or  ne^va 
came  to  be  called  the  posts.  The  name  has  retained  an  exact  ly 
eimilar  meaning  to  the  jjresent  day  in  most  parts  of  Europe,  aiid 
we  still  use  it  in  post-chaise,  post-boy,  post-horse  and  postillion. 
A  system  of  post  conveyance  for  letters  having  been  organized 
for  about  two  centuries  in  England  and  other  countries,  this  is 
perhaps  the  meaning  most  closely  associated  with  the  word  post 
at  present,  and  a  number  of  expressions  have  thus  arisen,  such 
as  post-office,  postage,  postal-guide,  postman,  postmaster,  postal- 
telegraph,  etc.  Curiously  enough  we  now  have  iron  letter-post» 
in  which  the  word  post  is  restored  exactly  to  its  original  meaning; 
Although  the  words  described  above  were  selected  on  accouiit 
of  the  curious  variety  of  their  meauings,  I  do  not  hesitate  1o 
assert  that  the  majority  of  common  nouns  possess  various 
meanings  in  greater  or  less  number.  Dr.  Watts,  in  bis  Logi.\ 
suggests  that  the  words  book,  bible,  fish,  house,  and  elephant,  are 
univocal  terms,  but  the  reader  would  easily  detect  ambiguities 
in  each  of  them.  Thus  fish  bears  a  very  different  meaning  iu 
natural  historj'  from  what  it  does  in  the  mouths  of  unscientific 
persons,  who  include  tinder  it  not  only  true  fishes,  but  shell-fisU 
or  mollusca,  and  the  cetacea,  such  as  whales  and  seals,  in  short 
all  swimming  animals,  whether  they  have  the  character  of  tru'3 
fish  or  not.  Elephant,  in  a  stationer's  or  bookseller's  shop,  means 
a  large  kind  of  paper  instead  of  a  large  animal.  Bible  some 
times  means  any  particular  copy  of  the  Bible,  sometimes  the 
collection  of  works  constituting  the  Holy  Scriptures.  The  word 
man  is  singularly  ambiguous ;  sometimes  it  denotes  man  as 
distinguished  from  woman  ;  at  other  times  it  is  certainly  used  to 
include  both  sexes  ;  and  in  certain  recent  election  cases  lawyers 
were  unable  to  decide  whether  tlie  word  man  as  used  in  the 
Reform  Act  of  1867  ought  or  ought  not  to  be  interpreted  so  as  to 
include  women.  On  other  occasions  man  is  used  to  denote  an 
adult  male  as  distinguished  from  a  boy,  and  it  also  often  denotee 
one  who  is  emphatically  a  man  as  possessing  a  masculine  char 
acter.  Occasionally  it  is  used  in  the  same  way  as  groom,  for  a 
servant,  as  in  the  y>roverb,  "'Like  master,  like  man."  At  other 
times  it  stands  specially  for  a  husband. 


B8  TESHS. 

(3)  Among  ambiguous  words  we  must,  thirdly,  dis- 
tiaguish  those  which  derive  their  various  meanings  in 
a  somewhat  differeut  manner,  namely  by  analogy  or 
real  resemblance.  When  we  speak  of  a  sweet  taste,  a 
Bweet  flower,  a  sweet  tune,  a  sweet  landscape,  a  sweet 
face,  a  sweet  poem,  it  is  evident  that  we  apply  one  and 
the  same  word  to  very  different  things ;  such  a  con- 
crete thing  as  lump-sugar  can  hardly  be  compared 
directly  with  such  an  intellectual  existence  as  Tenny- 
son's May  Qtieeti.  Nevertheless  if  the  word  sweet  is  to 
be  considered  ambiguous,  it  is  in  a  different  way  from 
those  we  have  before  considered,  because  all  the  things 
are  called  sweet  on  account  of  a  peculiar  pleasure  which 
they  jield,  which  cannot  be  described  otherwise  than 
by  comparison  with  sugar. 

In  a  similar  way,  we  describe  a  pain  as  sharp,  a  disappoint- 
ment as  bitter,  a  person's  temper  as  sour,  the  future  as  bright  or 
j^looniy,  an  acliievement  as  brilliant ;  all  these  adjt'Ctives  imply- 
ing comjjarison  with  bodily  sensations  of  the  simplest  kind. 
The  adjective  brilliant  is  derived  from  the  French  briUer,  to 
glitter  or  SDarkle ;  and  this  meaning  it  fully  retains  when  we 
speak  of  a  brilliant  diamond,  a  brilliant  star,  etc.  By  what  a 
subtle  analof^  is  it  that  we  speak  of  a  brilliant  position,  a 
brilliant  achievement,  brilliant  talents,  brilliant  style  I  We 
cannot  speak  of  a  clear  explanation.  Indefatigable  perseverance, 
perspicuous  style,  or  sore  calamity,  without  employing  in  each 
of  these  expressions  a  double  analogy  to  physical  impressions, 
actions,  or  events.  It  will  be  shown  in  the  fourth  8e<'tion  that 
to  this  proeesa  we  owe  the  creation  of  all  names  connected  with 
mental  feelings  or  exi^tencef 

Read  Watts'  Loffk,  Cliapter  IV. 

l>ocke's   Ennriy  on  the   Human    U'''»4er$tanding,  Book  IH 
Chapters  IX  and  X. 


EXTENSION  AND   INTENSION.  89 

In  this  section,  on  tlie  Ambiguity  of  Terms,  we 
liave  considered: — 

1.  Importance  of  Avoiding  Atnbiguity, 

2.  UnivoccU  and  Equivocal  Terms. 

3.  Kinds  and  Causes  of  Ambiguity, 


SECTIOIT  in* 

EXTENSION   AND   INTENSION. 

1.    Importance    of    Understandings   this   Double 
Meaning. 

There  is  no  part  of  the  doctrines  of  Logic  more 
necessary  to  be  understood  than  the  twofold  meaning 
of  terms  in  extension  and  intension.  The  learner  who 
acquires  a  thorough  apprehension  of  the  difference  of 
these  meanings,  and  learns  to  bear  it  always  in  mind, 
will  experience  but  little  further  difficulty  in  the  study 
of  Logic. 

2.  Meaning-  of  Extension  and  Intension. 

The  meaning  of  a  term  in  extension  consists  of  the 
objects  to  which  the  term  may  be  applied  ;  its  meaning 
in  intension  consists  of  the  qualities  which  are  necessa- 
rily possessed  by  objects  bearing  that  name.  A  simple 
example  will  make  this  distinction  most  apparent. 
What  is  the  meaning  of  the  name  "metal"?  The  first 
and  most  obvious  answer  is  that  metal  means  either 
gold,  or  silver,  or  iron,  or  copper,  or  aluminium,  or 
some  other  of  the  48  substances  known  to  chemists, 


ftO  TERMS. 

and  considered  to  have  a  metallic  nature.  These  Bub- 
atances  then  form  the  plain  and  common  meaning  of 
the  name,  which  is  the  meaning  in  extension.  But  if 
it  be  asked  why  the  name  is  applied  to  all  these  sub- 
stances and  these  only,  the  answer  must  be — Because 
they  possess  certain  qualities  which  belong  to  the  nature 
of  metal.  We  cannot,  therefore,  know  to  what  sub- 
stances we  may  apply  the  name,  or  to  what  we  may  not, 
unless  we  know  the  qualities  which  are  indispensable  to 
the  character  of  a  metal.  Now  chemists  lay  these  down 
to  be  somewhat  as  follows: — (1)  A  metal  must  be  an 
element  or  simi)le  substance  incapable  of  decomposition 
or  separation  into  simpler  substances  by  any  known 
means.  (2)  It  must  be  a  good  conductor  of  heat  and 
electricity.  (3)  It  must  possess  a  great  and  peculiar 
reflective  power  known  as  metallic  lustre.* 

These  j)roperties  are  common  to  all  metals,  or  nearly 
all  metals,  and  are  what  mark  out  and  distinguish  a 
metal  from  other  substances.  Hence  they  form  in  a 
certain  way  the  meaning  of  the  name  metal,  the  mean- 
ing in  intension,  as  it  is  called,  to  distinguish  it  from 
the  former  kind  of  meaning. 

In  a  similar  manner  almost  any  other  common  name  has  a 
double  meaning.  "  Stenmaliip  "  denotes  in  extension  the  Great 
Eastern,  the  Persia,  the  Himalaya,  or  any  one  of  the  thousands 
of  sfeam8hii>s  existing  or  which  have  existed  ;  in  intension  it 
menns  "  ii  vessel  pro|)elIod  by  steam-power."  Monarch  is  the 
name  of  Queen  Victoria.  Victor  Fmmanucl,  Louis  Napoleon,  or 
any  one  of  a  considerable  number  of  persons  who  rule  singly 

•  It  U  rtonbtfnlly  tnif  that  all  moinl«  posnecs  mclalUc  lnftro.andchemii»tfl 
woulil  find  It  very  diOlciilt  to  give  any  ronfiflciit  oxpliinntion  of  Uioir  ut^e 
nf  th<<  iiaiiH- ;  hat  the  statements  in  the  text  are  Bufllcientl^  trac  to  rumish  ac 
example. 


EXTENSION  AND   INTENSION.  41 

over  countries ;  the  persons  themselves  form  the  meaning  in 
extension  ;  the  quality  of  ruling  alone  forms  tlie  intensive  mean- 
ing of  the  name.  Animal  is  the  name  in  extension  of  any  one  of 
billions  of  existing  creatures  and  of  indefinitely  greater  numbers 
of  other  creatures  that  have  existed  or  will  exist ;  in  intension  it 
implies  in  all  those  creatures  the  existence  of  a  certain  animal 
life  and  sense,  or  at  least  the  power  of  digesting  food  and  exert 
ing  force,  which  are  the  marks  of  animal  nature. 

3.  Forms  of  Expressing  Exteusion  and  Intension. 

It  is  desirable  to  state  here  that  this  distinction  of 
extension  and  intension  has  been  explained  by  logicians 
under  various  forms  of  expression.  It  is  the  peculiar 
misfortune  of  the  science  of  logic  to  have  a  superflnity 
of  names  or  synonyms  for  the  same  idea.  Thus  the 
intension  of  a  term  is  synonymous  with  its  comprehen- 
sion, or  connotation,  or  depth ;  while  the  extension  is 
synonymous  with  the  denotation  or  breadth.  This  may 
be  most  clearly  stated  in  the  form  of  a  scheme : — 

The   extension,   extent,  The    intension,    intent, 

breadth,    denotation,    do-  depth,  connotation,  or  im- 

main,  sphere  or  application  plication   of  a  name  con- 

of  a  name  consists  of  the  sists  of  the   qualities   the 

individual  things  to  which  possession  of  which  by  those 

the  name  applies.  things  is  implied. 

Of  these  words,  denotation  and  connotation  are  employed 
chiefly  by  Mr.  J.  S.  Mill  among  modern  logical  writers,  and  are 
very  apt  for  the  purpose.  To  denote  is  to  mark  down,  and  tlie 
name  marks  the  things  to  which  it  may  be  applied  or  affixed; 
thus  metal  denotes  gold,  silver,  copper,  etc.  To  connote  is  to 
mark  along  with  (Latin  con,  together;  notare,  to  mark),  and  the 
connotation  accordingly  consists  of  the  qualities  before  described, 
the  possession  of  which  is  implied  by  the  use  of  the  name  metal 


iS  TSBHft. 

4.  The  Yariatiou  of  Extension  and  Intension. 

When  we  compare  different  but  related  terms  we  maj 
observe  that  they  differ  in  the  quantity  of  their  exten- 
sion and  intension.  Thus  the  term  element  has  a 
greater  extension  of  meaning  than  metal,  because  it 
includes  in  its  meaning  all  metals  and  other  substances 
as  well.  But  it  has  at  the  same  time  less  intension  of 
meaning  ;  for  among  the  qualities  of  a  metallic  substance 
must  be  found  the  qualities  of  an  element,  besides  the 
other  qualities  peculiar  to  a  metal.  If  again  we  com- 
pare the  terms  ynetal  and  malleable  metal,  it  is  apparen: 
that  the  latter  term  does  not  include  the  metals  anti- 
mony, arsenic,  and  bismuth,  which  are  brittle  sub- 
stances. Hence  malleable  metal  is  a  term  of  narrower 
meaning  in  extension  than  metal ;  but  it  has  also 
deeper  meaning  in  intension,  because  it  connotes  or 
implies  the  quality  of  malleability  in  addition  to  the 
general  ([ualities  of  a  metal.  White  malleable  metal  is 
again  a  narrower  term  in  extension  because  it  does  not 
include  gold  and  copper;  and  I  can  go  on  narrowing 
the  meaning  by  the  use  of  qualifying  adjectives  until 
only  a  single  metal  should  be  denoted  by  the  term. 

5.  The  Law  of  Variation. 

The  learner  will  now  see  clearly  that  a  general  law  of 
great  importance  connects  the  quantity  of  extension 
and  the  quantity  of  intension,  viz. — As  the  intension  of 
a  term  is  increased  the  extension  is  decreased.  It 
must  nut  be  supjwscd,  indeed,  that  there  is  any  exact 
proportion  Ixjtween  the  degree  in  which  one  meaning 


EXTENSION  AND  INTENSION.  48 

IS  increased  and  the  other  decreased.  Thus  if  we  join 
the  adjective  red  to  metal  we  narrow  the  meaning  much 
more  than  if  we  join  the  adjective  white,  for  there  are 
at  least  twelve  times  as  many  Avhite  metals  as  red. 
Again,  the  term  white  man  includes  a  considerable 
fraction  of  the  meaning  of  the  term  man  as  regards 
extension,  but  the  term  blind  man  only  a  small  frac- 
tion of  the  meaning.  Thus  it  is  obvious  that  in 
increasing  the  intension  of  a  term  we  may  decrease  the 
extension  in  any  degree. 

In  understanding  this  law  we  must  carefully  discriminate  the 
cases  where  there  is  only  an  apparent  increase  of  the  intension 
of  a  term,  from  those  where  the  increase  is  real.  If  I  add  the 
term  elementary  to  meted,  I  shall  not  really  alter  the  extension 
of  meaning,  for  all  the  metals  are  elements  ;  and  the  elementary 
metals  are  neither  more  nor  less  numerous  than  the  metals.  But 
then  the  intension  of  the  term  is  really  unaltered  at  the  same 
lime ;  for  the  quality  of  an  element  is  really  found  among  the 
qualities  of  metal,  and  it  is  superfluous  to  specify  it  over  again. 
A  quality  which  belongs  invariably  to  the  whole  of  a  class  of 
things  is  commonly  called  a  property  of  the  class,  and  we  cannot 
qualify  or  restrict  a  term  by  its  own  property. 

6.  Connotative  and  Non-connotative  Terms. 

This  is  a  convenient  place  to  notice  a  distinction 
between  terms  into  those  which  are  connotative  and 
those  which  are  non-connotative,  the  latter  consisting 
of  the  terms  which  simply  denote  things  without  imply- 
ing any  knowledge  of  their  qualities. 

As  Mr.  Mill  considers  this  distinction  to  be  one  of  great 
importance,  it  will  be  well  to  quote  his  own  words  :— 

"  A  non-connotative  term  is  one  wliich  signifies  a  subject  only, 
or  an  attribute  only.     A  connotative  term  is  one  which  denotes  a 


44  TBRHS. 

subject,  and  implies  an  attribute.  B7  a  subject  is  here  meant 
anything  uiiich  possesst's  attributes.  Tlius  John,  or  London,  or 
England,  are  mimes  which  signify  a  subjtct  only.  Whiteness, 
lengtli,  virtue,  signify  an  attribute  only.  None  of  these  names, 
therefore,  are  cnnnotative.  But  white,  long,  virtuous,  are  conno- 
tative.  Tlie  word  wliite  denotes  all  white  tilings,  as  snow,  paper, 
the  foam  of  the  sen,  etc.,  and  implies,  or,  as  it  was  termed  by  the 
schoolmen,  connotes  the  attribute  whiteness.  The  word  white  is 
not  predicated  of  the  attribute,  but  of  the  subjects,  snow,  etc. ; 
but  when  we  predicate  it  of  them,  we  imply,  or  connote,  that  thi 
attribute  wliiteness  belongs  to  them 

"  All  concrete  general  names  are  connotative.  The  word 
man,  for  example,  denotes  Peter,  James,  John,  and  an  indefinite 
number  of  other  individuals,  of  whom,  taken  as  a  class,  it  is 
the  name.     But  it  is  applied  to  them,  because  they  possess,  and 

to  signify  that  they  possess,  certain  attributes What  we  call 

men,  are  tiie  subjects,  the  individual  Styles  and  Nokes  ;  not  the 
qualities  by  which  tlieir  liumanity  is  constituted.  The  name, 
therefore,  is  said  to  signify  the  subjects  directly,  the  attributes 
indirectly  ;  it  denotes  the  subjects,  and  implies,  or  involves,  or 
indicates,  or,  as  we  shall  say  iienceforth,  connotes,  the  attri- 
butes.    It  is  a  connotative  name 

'Proper  names  are  not  connotative:  they  denote  the  indl 
viduftls  who  are  culled  by  them  ;  but  they  do  not  indicate  or  im- 
ply any  attributes  as  Ijelonging  to  those  individuala  When  we 
name  a  child  by  the  name  Paul,  or  a  dog  by  the  name  Caesar, 
these  nan^s  are  simply  marks  used  to  enable  those  individuals 
to  be  made  subjects  of  disaiurse.  It  may  bt^  said,  indeed,  that 
we  must  have  liad  some  reason  for  giving  them  those  names 
rather  than  any  others ;  and  this  is  true ;  but  the  name,  once 
given,  is  independent  of  the  reason.  A  man  may  have  been 
named  John,  because  that  was  the  name  of  his  father;  a  town 
may  have  been  named  Dartmouth,  because  it  is  situated  at  the 
month  of  the  Dart.  But  it  is  no  part  of  the  signification  of  th» 
word  John,  that  the  father  of  the  person  so  called  bore  the  samo 
name  ;  nor  even  of  the  woni  Dartmouth,  to  be  situated  at  the 
mouth  of  the  Dart.  If  sand  should  choke  up  the  mouth  of  the 
river,  or  an  earthquake  change  its  course,  or  remove  it  to  a  di» 


EXTENSION   AND  INTENSION.  46 

tance  from  the  town,  the  name  of  the  town  would  not  nece88ari];f 
be  changed. "  * 

I  quote  this  in  Mr.  Mill's  osvn  words,  because  though  it  ex- 
presses most  clearly  the  view  accepted  by  Mr.  Mill  uud  manj 
others,  it  is  nevertheless  probabiy  erroneous.  The  couuotaiion 
of[a  name  is  conlused  witli  the  etymological  meaning,  or  the  cir 
cumstaiices  which  caused  it  to  be  affixed  lo  a  thing.  Surely  no 
one  who  uses  the  name  England,  and  knows  what  it  denotes,  can 
be  ignorant  of  the  pecidiar  qualities  and  circunifatauces  of  the 
country,  and  these  form  the  connotation  of  the  term.  To  any 
one  who  knows  the  town  Dartmouth  the  name  must  imply  the 
possession  of  the  circumstances  by  which  tluit  town  is  character- 
ized at  the  present  time.  If  the  river  Dart  should  be  destKned 
or  removed,  the  town  would  so  far  be  altered,  and  the  siguilica 
tion  of  the  name  changed.  The  name  would  no  longer  denote  a 
town  situated  on  the  Dart,  but  one  which  was  foivnerly  situated 
on  the  Dart,  and  it  would  be  by  a  mere  historical  accident  that  the 
form  of  the  name  did  not  appear  suitable  to  the  town.  So  again 
any  proper  name,  such  as  John  Smith,  is  almost  without  mt  aniug 
until  we  know  the  John  Smith  in  question.  It  is  true  that  the 
name  alone  connotes  the  fact  that  he  is  a  Teuton,  and  is  a  male; 
but,  so  soon  as  we  know  the  exact  individual  it  denotes,  the 
name  surely  implies,  also,  the  peculiar  features,  form,  and  charac- 
ter, of  that  individual.  In  fact,  as  it  is  only  by  the  peculiar 
qualities,  features,  or  circumstances  of  a  thinpr,  that  we  can 
ever  recognize  it,  no  name  could  have  any  fixed  meaning  unless 
we  attached  to  it,  mentally  at  least,  such  a  definition  of  the  kind 
of  thing  denoted  by  it,  that  we  should  know  whether  any  given 
thing  was  denoted  by  it  or  n)t.  If  the  name  of  John  Smith  does 
not  suggest  to  my  mind  the  qualities  of  John  Smith,  how  shall  I 
know  him  when  I  meet  him  ?  for  he  certainly  does  not  bear  his 
name  written  upon  his  brow. 

Abstract  names,  on  the  other  hand,  can  hardly  possess  conno- 
tation at  all,  for  as  they  already  denote  the  attributes  or  qualities 
of  something,  there  is  nothing  left  which  can  form  the  connota- 
tion of  the  name.     Mr.  Mill,  indeed,  thinks  that  abstract  names 

*  System  qf  Logic,  YoL  I,  p.  31,  sixth  editisn.    Book  I,  Ctutp.  IL 


46  TEBMB. 

may  often  be  considered  connotative,  as  when  the  name  JaniiK 
connotes  the  attribute  of  hurtfulness  as  belonging  to  fault.  But 
if  fault  is  a  true  abstract  word  at  all  1  should  regard  hurtfulness 
as  a  part  of  its  denotation  ;  I  am  inclined  to  think  that  faultineti 
is  the  abstract  name,  and  that  fault  is  generally  used  concretely 
as  the  name  of  a  particular  action  or  thing  that  is  faulty,  or  ix)& 
sesses  faultiness.  But  tlie  subject  cannot  be  properly  discussed 
here,  and  the  reader  should  note  Mr.  Mill's  opinion  that  abstract 
names  are  usually  non-connutative,  but  may  be  connotative  in 
some  cases. 
The  subject  of  Extension  and  Intension  may  be  pursued  in 

Hamilton's  Lectures  on   Logic,  Lect.  Vlll. ;  or    in  Thom 

son's  Laws  of  Thought,  Sections  48  to  52. 

In  this  scctiou,  on  Extension  and  Intension,  we 
bave  considered  :— 

1.  The  Importance  of  Underatanding  this  Double 

Meaning. 

2.  The  Meaning  of  Extension  and  Intension. 

3.  T?ie  Forms  of  Expressing  Extension  and  In' 

tension. 

4.  The  Variation  of  Extension  and  Intension, 
6.  The  Law  of  Variation. 

6.  Connotative  and  Non-connotative  Terms, 


SECTION  lY. 

THE   GROWTH    OF   LANGUAGE. 

1.  The  Two  Principal  Processes  of  Growth. 

Words,  we  have  seen,  become  eqnivocal  in  at  least 
throe  different  ways — by  the  accidental  confusion  of 
different  words,  by  the  chanj^e  of  meaning  of  a  word 
by  its  habitual  association  with  other  things  than  its 
original  meaning,  and  by  analogical  transfer  to  objects 
'>f  %  similar  nature.     We  must,  however,  consider  some* 


THE   GROWTH   OF   LANGUAGE.  47 

what  more  closely  certain  changes  in  language  wliich 
arise  out  of  the  last  cause,  and  which  ai*e  in  constant 
progress.  We  can  almost  trace,  in  fact,  the  way  in 
wiiich  language  is  created  and  extended,  and  the  sub- 
ject is  to  the  logician  one  of  a  highly  instructive  and 
important  character.  There  are  two  great  and  con- 
trary processes  which  modify  language,  as  follows: 

(1)  Generalization,  by  which  a  name  comes  to  be 
applied  to  a  wider  class  of  objects  than  before,  so  that 
the  extension  of  its  meaning  is  increased,  and  the  in- 
tension diminished. 

(2)  Specialization,  by  which  a  name  comes  to  be 
restricted  to  a  narrower  class,  the  extension  being  de- 
creased and  the  intension  increased. 

2.  Generalization. 

The  first  change  arises  in  the  most  obvious  manner, 
from  our  detecting  a  resemblance  between  a  new  object, 
which  is  without  a  name,  and  some  well-known  object. 
To  express  the  resemblance  we  are  instinctively  led  to 
apply  tlie  old  name  to  the  new  object.  Thus  we  are 
well  acquainted  with  glass,  and,  if  we  meet  any  sub- 
stance having  tlie  same  glassy  nature  and  appearance, 
we  shall  be  apt  at  once  to  call  it  a  kind  of  glass;  should 
we  often  meet  with  this  new  kind  of  glass  it  would 
probably  come  to  share  the  name  equally  with  the  old 
and  original  kind  of  glass.  The  word  coal  has  under- 
gone a  change  of  this  kind  ;  originally  it  was  the  name 
of  charked  or  cliarred  wood,  which  was  the  principal 
kind  of  fuel  used  five  hundred  years  ago.  As  mineral 
coal  came  into  use  it  took  the  name  from  the  former 
fuel,  which  it  resembled  more  nearly  than  anything 
else,  but  was  at  first  distinguished  as  sea-coal  or  pit- 


48  TERMS. 

coal.     Being  now  far  the  more  common  of  the  two,  it 

has  taken  the  simple  name,  and  we  distinguish  charred 
wood  rts  charcoal.  Paper  has  undergone  a  like  change ; 
originally  denoting  the  papyrus  used  in  the  Roman 
empire,  it  was  transferred  to  the  new  writing  material 
made  of  cotton  or  linen  rags,  which  was  introduced  at 
a  quite  uncertain  period.  The  word  character  is  inter- 
esting on  account  of  its  logical  employment ;  the  Greek 
XapaKTrip  denoted  strictly  a  tool  for  engraving,  but  it 
became  transferred  by  association  to  the  marks  or  letters 
engraved  with  it,  and  this  meaning  is  still  retained  by 
the  word  when  we  speak  of  Greek  characters,  Arabic 
characters,  i.  e.,  figures  or  letters.  But  inasmuch  as 
objects  often  have  natural  marks,  signs,  or  tokens, 
which  may  indicate  them  as  well  as  artificial  characters, 
the  name  was  generalized,  and  now  means  any  peculiar 
or  distinctive  mark  or  quality  by  which  an  object  ia 
easily  recognized. 

Changes  of  this  kind  are  usually  effected  bj  no  particular  per- 
son and  witli  no  distinct  purpose,  but  by  a  sort  of  unconscious 
instinct  in  u  number  of  ])crs<>ns  using  the  name.  In  the  language 
of  science,  liowcver,  changes  are  often  made  purposely,  and 
vnili  11  clear  apprehension  of  the  generalization  implied.  Thus 
toap  in  ordinary  life  is  api)lit?d  only  to  a  comi)Ound  of  soda  or 
pota.sh  with  fat;  but  chemists  have  pur|)osoly  extended  the  name 
so  as  io  include  any  compound  of  a  metallic  salt  with  a  fatty  sub- 
rttance.  Accordingly  there  are  such  things  as  hme  aoop  and  lead- 
Hoap,  which  latter  is  employed  in  making  common  diacliyloo 
pjaater.  Alohol  at  first  denoted  the  pnxluctof  ordinary  fermen- 
tation c<miini»nly  called  spirits  of  wine,  but  chemists  having  dis 
covered  that  njany  other  substances  had  a  thi-oreticAl  composition 
closely  resembling  spirits  of  wine,  the  name  was  adopted  for  the 
whole  class,  and  a  long  enumeration  of  different  kinds  of  alco- 
hols will  Ix;  found  in  l)r,  Roscoe's  lessons  on  chemistry.     The 


THE  QiOWTH   OF  LANGLAQK.  49 

Dumber  of  known  alcohols  is  likewise  subject  to  indefinite  increase 
by  the  progress  of  discovery.  Every  one  of  tlie  chemical  teruiH 
acid,  alkali,  metul,  alloy,  earth,  uther,  oil,  gas,  salt,  may  be 
ihown  to  have  uudergoue  great  generalizations.  In  othei 
sciences  there  is  hardly  a  less  supply  of  instances.  A  lens 
originally  meant  a  lenticular  shaped  or  double  convex  piece  of 
glass,  that  being  the  kind  of  glass  most  frequently  used  by 
opticians.  But  as  glasses  of  other  shaiics  came  to  be  used  along 
with  lenses,  the  name  was  extended  to  concave  or  even  to  per- 
fectly flat  piec.!S  of  glass.  The  words  lever,  plane,  cone,  cylinder, 
arc,  conic  section,  curve,  prism,  magnet,  pendulum,  ray,  light,  and 
many  others,  have  been  similarly  generalized. 

In  common  language  we  may  observe  that  even  proper  or 
singular  names  are  often  generalized,  as  when  in  the  time  of 
Cicero  a  good  actor  was  called  a  Roscius  after  an  actor  of  pre. 
eminent  talent.  The  name  Caesar  was  adojited  by  the  successor 
of  Julius  Caesar  as  an  official  name  of  the  emperor,  with  which  it 
gradually  became  synonymous,  so  that  in  the  present  day  the 
Kaisers  of  Austria  and  the  Czars  oi  Russia  both  take  their  title 
from  Caesar.  Even  the  abstract  name  Caesarism  has  been  formed 
to  express  a  kind  of  imperial  system  as  established  by  Caesar 
The  celebrated  tower  built  by  a  king  of  Egypt  on  the  island  Oi 
Pharos,  at  the  entrance  of  the  harbor  of  Alexandria,  has  caused 
lighthouses  to  be  called  phares  in  French,  and  pharos  in  olisolete 
English.  From  the  celebrated  Roman  General  Quintus  Fabius 
Maximus  any  one  who  avoids  bringing  a  contest  to  a  crisis  is  said 
to  pursue  a  Fabian  policy. 

In  science  also  singular  names  are  often  extended,  as  when 
the  fixed  stars  are  called  distant  S7ins,  or  the  compan'-^ns  of 
Jupiter  are  called  his  moons.  \t  is  indeed  one  theory,  and  a 
probable  one,  that  all  general  names  were  created  by  the  process 
nf  generalization  going  on  in  the  early  ages  of  human  progress. 
As  the  comprehension  of  general  notions  requires  higher  intellect 
than  the  apprehension  of  singular  and  concrete  things,  it  seems 
natural  that  names  should  at  first  denote  individual  objects,  and 
should  afterwards  be  extended  to  classes.  We  have  a  glimpse 
of  this  process  in  the  case  of  the  Australian  natives  who  had 
been  accustomed  to  call  a  large  dog  CacUi,  but  when  horses  wer» 


IK)  TERMS. 

first  introduced  into  the  country  they  adopted  this  name  as  ths 
neatest  description  of  u  horse.  A  very  similar  incident  is  re- 
lated by  Captain  Cook  of  the  natives  of  Otaheite.  It  may  be  ob 
jected,  however,  that  a  certain  process  of  judgment  must  have 
been  exerted  before  the  suitability  of  a  name  to  a  particular 
thing  could  have  been  i)erceived,  and  it  may  be  o^nsidered 
probable  that  specialization  as  well  as  generalization  must  liave 
acted  in  the  earliest  origin  of  language  much  as  it  does  at 
present. 

3.  Specialization. 

Si>ecialization  is  an  exactly  opposite  process  to  gener- 
alization and  is  almost  equally  important.  It  consists 
in  narrowing  the  extension  of  meaning  of  a  general 
name,  so  that  it  comes  to  be  the  name  only  of  an 
inelividual  or  a  minor  part  of  the  original  class.  It  is 
thus  we  are  furnished  with  the  requisite  names  for  a 
multitude  of  new  implements,  occupations  and  ideas 
with  which  we  deal  in  advancing  civilization.  The 
name  physician  is  derived  from  the  Greek  (pvatKoc, 
natural,  and  (pvaig,  nature,  so  that  it  properly  means 
one  who  has  studied  nature,  especially  the  nature  of 
the  human  body.  It  has  become  restricted,  however, 
to  those  who  use  this  knowledge  for  medical  jmrposes, 
and  tlie  investigators  of  natural  science  have  been 
obliged  to  adopt  the  new  name  physicist.  The  name 
naturalist  has  been  similarly  restricted  to  those  who 
study  animated  nature.  The  name  surgeon  originally 
lucant  handicraftsman,  being  a  corruption  o^chirurgeoii, 
lerived  from  the  Greek  ;^«^jowpy6f,  hand-worker.  It 
nas  long  been  8i)ecialized,  however,  to  those  who  per- 
form the  mechanical  parts  of  the  sanatory  art. 

lianfriiiige  abounds  with  other  examples.  Minister  originaJly 
meant  a  servant,  or  one  who  acted  as  a  minor  of  another.     Not* 


THB  aBOWTH  OF  LANaUAQB.  51 

It  often  means  specially  the  most  important  man  in  the  kingdom 
A  chancellor  was  a  clerk  or  even  u  door-keeper  who  sat  in  a  placa 
separated  by  bars  or  canceUi  in  tlie  offices  of  tiie  Roman  em- 
peror's palace  ;  now  it  is  always  the  name  of  a  high  or  even  the 
highest  dignitary.  Peer  was  an  equal  (Latin,  Par),  and  we  still 
speak  of  being  tried  by  our  peers  ;  but  now,  by  the  strange  acci- 
dents of  language,  it  means  the  few  who  are  superior  to  the  rest 
of  the  Queen's  subjects  in  rank.  Deacon,  Bisliop,  Clerk,  Queen, 
Captain,  General,  are  all  words  which  have  undergone  a  like 
process  of  specialization.  In  such  words  as  telegraph,  rail, 
signal,  station,  and  many  words  relating  to  new  inventions,  wa 
may  trace  the  progress  of  change  in  a  lifetime. 

4.  Desyuouyinizatiou, 

One  effect  of  the  process  of  specialization  is  very  soon 
to  create  a  difference  between  any  two  words  which 
happen  from  some  reason  to  be  synonymous.  Two  or 
more  words  are  said  to  be  synonymous  (from  tlie  Greek 
ovv^  with,  and  ovoiia,  name)  when  they  have  the  same 
meaning,  as  in  the  case,  perhaps,  of  teaclier  and  in- 
structor, similarity  and  resemblance,  beginning  and 
commencement,  sameness  and  identity,  hypothesis  and 
supposition,  intension  and  comprehension.  But  the 
fact  is  that  words  commonly  called  synonymous  are 
seldom  perfectly  so,  and  there  are  almost  always 
shades  of  difference  in  meaning  or  use,  which  are  ex- 
plained in  such  works  as  Crabb's  English  Sifnonyms. 
A  process  called  by  Coleridge  desynonymization,  and  by 
Herbert  Spencer  differentiation,  is  always  going  on, 
which  tends  to  specialize  one  of  a  pair  of  synonymous 
words  to  one  meaning  and  the  other  to  another.  Thus 
wave  and  billow  originally  meant  exactly  the  same 
physical  effect,  but  poets  have  now  ajipropriated  the 
word  "  billow,"  whereas  wave  is  used  chieiiy  m  practicai 


52  TERMS. 

and  scientific  matters.  Undulation  is  a  third  83rnonym, 
which  will  probably  become  the  sole  scientific  term  for 
a  wave  in  course  of  time.  Cab  was  originally  a  mere 
abbreviation  of  cabriolet,  and  therefore  of  similar  mean- 
ing, but  it  is  now  specialized  to  mean  almost  exclusively 
u  hackney  cab.  In  America  car  is  becoming  restricted 
to  the  meaning  of  a  railway  car. 

It  may  be  remarked  that  to  possess  a  great  number  of  syn- 
onymous terms  is  a  logical  defect  in  a  language,  since  we 
acquire  the  habit  of  using  them  indifferently  without  being  sure 
that  they  are  not  subject  to  ambiguities  and  obscure  differences 
of  meaning.  The  English  language  is  especially  subject  to  the 
inconvenience  of  having  a  complete  series  of  words  derived  from 
Greek  or  Latin  roots  nearly  synonymous  with  other  words  of 
Saxon  or  French  origin.  The  same  statement  may,  in  fact,  be 
put  into  Saxon  or  classical  English  ;  and  we  often,  as  Whately 
has  wtll  remarked,  seem  to  prove  a  statement  by  merely  repro- 
ducing it  in  altered  language.  The  rhetorical  power  of  the 
language  may  be  increased  by  the  copiousness  and  variety  of 
diction,  but  pitfalls  are  thus  prepared  for  all  kinds  of  fallacies. 

5.  Metaphorical  Kxtension  of  Meaning^. 

In  addition  to  the  effects  of  generalization  and  speci- 
alization, vast  additions  and  changes  are  made  in  lan- 
guage by  the  process  of  metaphorical  extension  of  the 
meaning  of  words.  This  change  may  be  said,  no  doubt, 
to  consist  in  generalization,  since  there  must  always  be 
a  resemblance  between  the  new  and  old  applications  of 
the  term.  But  the  resemblance  is  often  one  of  a  most 
distant  and  obscure  kind,  such  as  we  should  call  analogy 
rather  than  identity.  All  words  used  metaphorically, 
or  as  similitudes,  are  cases  of  this  process  of  extension. 
The  name  metaphor  is  derived  from  the  Greek  wordi 


IKE  GROWTH  OF  LANGUAGE.  51 

fterd,  over,  and  <pspeiv,  to  carry ;  and  expresses  appar- 
ently the  transference  of  a  word  from  its  ordinary  to  a 
peculiar  purpose.  Thus  the  old  simiUtude  of  a  ruler  to 
the  pilot  of  a  vessel  gives  rise  to  many  metaphors,  as  in 
speaking  of  the  prime  minister  being  at  the  helm  of 
the  state.  The  word  governor,  and  all  its  derivatives, 
is,  in  fact,  one  result  of  this  metaphor,  being  merely  a 
corrupt  form  oi  gubernator,  steersman. 

The  words  compass,  polestar,  ensign,  anchor,  and  many  others 
connected  with  navigation,  are  constantly  used  in  a  metapliorical 
manner.  From  the  use  of  horses  and  hunting  we  derive  another 
set  of  metaphors  ;  as,  in  taking  the  reins  of  government,  over- 
turning the  government,  taking  the  bit  between  the  teeth,  the 
government  whip,  being  heavily  weighted,  etc.  No  doubt  it 
might  be  shown  that  every  other  important  occupation  of  life  has 
furnished  its  corresponding  stock  of  metaphors. 

6.  Origin  of  the  Mental  Vocabulary. 

This  process,  besides  going  on  consciously  at  the 
present  day,  must  have  acted  throughout  tlie  history  of 
language,  and  we  owe  to  it  almost  all,  or  probably  all, 
the  words  expressive  of  refined  mental  or  spiritual  ideas. 
The  very  word  spirif,  now  the  most  refined  and  imma- 
terial of  ideas,  is  but  the  Latin  spi'ritus,  a  gentle  breeze 
or  breathing  ;  and  inspiration,  esprit,  or  wit,  and  many 
other  words,  are  due  to  this  metaphor.  It  is  truly 
curious,  however,  that  almost  all  the  words  in  different 
languages  denoting  mind  or  soul  imply  the  same 
analogy  to  breath.  Thus,  soul  is  from  the  Gothic  root 
denoting  a  strong  wind  or  storm  ;  the  Latin  words 
animus  and  anima  are  supposed  to  be  connected  with 
the  Greek  aveuoq,  wind  ;  V"^;t'7  is  certainly  derived  froiw; 


64  TEBK8. 

t/>v;^w,  to  blow ;  irvevna,  air  or  breath,  is  used  in  th« 
New  Testament  for  Spiritual  Being;  and  our  word 
ghost  has  a  similar  origin. 

Almost  all  the  terms  employed  in  mental  philosophy  or 
metaphysics,  to  denote  actions  or  phenomena  of  mind,  are  ulti- 
mat  'ly  derived  from  metaphors.  Apprehension  is  the  putting 
forward  of  the  hand  to  take  anything ;  comprehension  is  the 
taking  of  things  together  in  a  handful ;  extension  is  the  spread- 
ing out;  intention,  the  bending  to;  explication,  the  unfolding; 
application,  the  folding  to;  conception,  the  taking  up  together; 
relation,  tlie  carrying  back  ;  experience  is  the  thoroughly  going 
through  a  thing ;  difiference  is  the  carrying  apart  ;  deliberatioa 
the  weighing  out :  interruption,  the  breaking  between  ;  proposi- 
tioa  the  placing  before  ;  intuition,  the  seeing  into  ;  and  the  list 
miglit  be  almost  indefinitely  extended.  Our  English  name  for 
reason,  the  understanding,  obviously  contains  some  physica. 
metaphor  which  has  not  been  fully  explained  ;  with  the  Latin 
intellict  tliere  is  also  a  metaphor; 

Every  sense  gives  rise  to  words  of  refined  meaning ;  sapience^ 
taste,  insipidity,  gout,  are  derived  from  the  sense  of  taste  ;  saga, 
city,  from  the  dog's  extraordinary  iwwer  of  smell ;  but  as  the 
sense  of  sight  is  by  far  the  most  acute  and  intellectual,  it  gives 
rise  to  the  larger  part  of  language  ;  clearness,  lucidity,  obscurity, 
haziness,  perspicuity,  and  innumerable  other  expressions,  ar* 
derived  from  this  sense. 

7.  The  Fertility  of  Root-words. 

It  is  truly  astonishing  to  notice  the  power  which 
language  possesses  by  the  processes  of  generalization, 
3{)ecialization,  and  metaphor,  to  create  many  words 
from  one  single  root.  Prof.  Max  Muller  has  given  n 
remarkable  instance  of  this  in  the  case  of  the  root 
spec,  which  means  siriht,  and  appears  in  the  Aryan  Ian- 
gnages,  as  in  the  Sanscrit  spas,  the  Greek  aKenTOfuUf 


THE  OBOWTH  OF  LANOUAOE.  M 

with  transposition  of  consonants,  in  the  Latin  specio, 
and  even  in  the  English  spy. 

The  fullowing  is  an  incomplete  list  of  the  words  developed 
from  this  one  root ;  species,  special,  especial,  specimen,  spice, 
spicy,  specious,  speciality,  8i)ecific,  specialization,  specie  (gold,  or 
silver),  spectre,  specification,  spectacle,  spectator,  spectral,  spec- 
trum, speculum,  specular,  speculation.  The  same  root  also  enters 
into  composition  with  various  prefixes ;  and  we  thus  obtain  a 
series  of  words,  suspect,  aspect,  circums[)ect,  expect,  inspect, 
prospect,  respect,  retrospect,  introspection,  conspicuous,  perspi- 
cuity, perspective  ;  with  each  of  which,  again,  a  numlier  of  de- 
rivatives is  connected.  Thus,  from  suspect,  we  derive  suspicioa 
suspicable,  suspicious,  suspiciously,  suspiciousness.  I  have  esti- 
mated that  there  are  in  all  at  least  246  words,  employed  at  some 
period  or  other  in  the  English  language,  which  undoubt«;d]y 
Dome  from  the  one  root  spec. 

J.  S.  Mill's  Logic,  Book  IV,  Chap.  V,  "  On  the  Natural  History 

of  the  Variations  in  the  Meanings  of  Terms." 
Archbishop  Trench,  On  the,  Study  of  Words. 
Max  Miiller,  Lectures  on  the  Science  of  Language. 
Whitney's  Life  and  Qrowth  of  Language. 

In   this   section,    on    "Tlie    Growth    of    Lan 
guage,'*  we  have  considered : — 

1.  The  Two  Principal  Processes  of  GrowtJi. 

2.  GeneraUzation. 

3.  Specialization. 

4.  Desi/iionyniization. 

6.    Metaphorical  Extension  of  Meaning. 
6.    Orif/in  of  the  Mental  Vocabalar/^. 
I.   The  Fertility  of  Root-words, 


S6  rBBM& 


SECTION   Y. 

THE     PERFECT    AND     THE    IMPERFECT 
KNOWLEDGE    OF    TERMS. 

1.  Statement  of  the  Question. 

In  treating  of  Terms  it  is  necessary  that  we  should 
clearly  understand  what  a  perfect  notion  of  the  mean- 
ing of  a  term  requires.  When  a  name  such  as  monarch, 
or  civilization,  or  autonomy  is  used,  it  refers  the  mind 
to  some  thing  or  some  idea,  and  we  ought,  if  possible, 
to  obtain  a  perfect  knowledge  of  the  thing  or  idea  be- 
fore we  use  the  word.  In  what  does  this  perfect  knowl- 
edge consist  ?     What  are  its  necessary  characters  ? 

This  is  a  question  which  the  celebrated  matheinatician  and 
philo8oi)her  Leibnitz  attempted  to  anssver  in  a  small  treatise  or 
tract  first  published  in  the  year  1684.  This  tract  has  been  the 
basis  of  what  is  given  on  the  subject  in  several  recent  works 
on  Logic,  and  a  complete  translation  of  the  tract  has  been 
appended  by  Mr.  Baynes  to  his  translation  of  the  Port  Royal 
Logic.  As  the  remarks  of  Leibnitz  himself  are  not  always  easy 
to  understand,  I  will  not  confine  myself  to  his  exact  words,  but 
will  endeavor  to  give  the  simplest  possible  statement  of  his  views, 
according  as  they  have  been  interpreted  by  Dr.  Thomson  or  Sir 
W.  Hamilton. 

2.  Scheme  of  Distinctions. 

Knowledge  is  either  obscure  or  clear;  either  con* 
rtised  or  distinct ;  eitlier  adequate  or  inadequate  ;  and 
lastly,  either  symbolical  or  intuitive.  Perfect  knowledge 
must   be  clear,  distinct,  adequate  and  intuitive ;  if  it 


KNOWLEDGE   OF  TERMS.  67 

fails  in  any  of  these  respects  it  is  more  or  less  Imper 
feet.  We  may,  therefore,  classify  knowledge  as  in  the 
following  scheme : — 

Knowledge 

Clear  Obscure 


Distinct  Confused 

Adequate  Inadequate 

Intuitive  Symbolical 

Perfect.  Imperfect. 

(1)  Clear  and  Obscure  Knowledge  Distinguished. — 

A  notion,  that  is  to  say  our  knowledge  of  a  thing, 
is  obscure  when  it  does  not  enable  us  to  recognize 
the  thing  again  and  discriminate  it  from  all  other 
things.  We  have  a  clear  notion  of  a  rose  and  of  most 
common  flowers  because  we  can  recognize  them  with 
certainty,  and  do  not  confuse  them  with  each  other. 
Also  we  have  a  clear  notion  of  any  of  our  intimate 
friends  or  persons  whom  we  habitually  meet,  because 
we  recognize  them  whenever  we  see  them  with  the 
utmost  certainty  and  without  hesitation. 

It  is  said  that  a  shepherd  acquires  bv  practice  a  clear  notion  of 
each  sheep  of  his  flock,  so  as  to  enable  him  to  single  out  any  one 
separately,  and  a  keeper  of  hounds  learns  the  name  and  character 
of  each  hound,  while  otlier  persons  have  only  an  obscure  idea  of 
the  hounds  generally,  and  could  not  discriminate  one  from  the 
other.  But  the  geologist  cannot  give  a  clear  idea  of  what  sand- 
stone, conglomerate,  or  schist,  or  slate,  or  trap  rock  consists,  be- 
cause different  rocks  vary  infinitely  in  degree  and  character,  and 
it  is  often  barely  possible  to  say  whether  a  rock  is  sandstone  ol 


58  TERMS. 

conglomerate,  schist  or  slate,  and  so  on.  In  the  lower  forms  ol 
life  the  naturalist  liardlj  has  a  clear  notion  of  animal  life,  as  di^ 
tinguished  from  vegetable  life ;  it  is  often  difficult  to  decide 
whether  a  protophyte  should  be  classed  with  animals  or  plants. 

(2)  Distinct  and  Confused  Knowledge  Distinguished. 

—Clear  knowledge,  again,  is  confused,  when  we  ciumot 
distinguish  the  parts  and  qualities  of  the  thing  known, 
and  can  only  recognize  it  as  a  whole.  Though  any  one 
instantly  knows  a  friend,  and  could  discriminate  him 
from  all  other  persons,  yet  he  would  generally  find  it 
impossible  to  say  how  he  knows  him,  or  by  what 
marks.  He  could  not  describe  his  figure  or  features, 
but  in  the  very  roughest  manner.  A  person  unpractised 
in  drawing,  who  attempts  to  delineate  even  such  a 
familiar  object  as  a  horse  or  cow,  soon  finds  that  he  has 
but  a  confused  notion  of  its  form,  while  an  artist  has  a 
distinct  idea  of  the  form  of  every  limb.  The  chemist 
has  a  distinct  as  well  as  a  clear  notion  of  gold  and  silver, 
for  he  can  not  only  tell  with  certainty  whether  any 
metal  is  really  gold  or  silver,  but  he  can  specify  and 
describe  exactly  the  qualities  by  which  he  knows  it; 
and  could,  if  necessary,  mention  a  great  many  other 
qualities  as  well. 

We  have  a  very  distinct  notion  of  a  chess-board,  because 
we  know  it  consists  of  64  square  spaces  ;  and  all  our  ideas  ol 
geometrical  figures,  such  as  triangles,  circles,  parallelograms, 
squares,  pentagons,  hexagons,  etc.,  are  or  ought  to  be  perfectly 
Hstinct.  But  when  we  talk  of  a  covnUtutionnl  gorernment,  or  a 
nnUizfd  nation,  we  have  only  the  vagiu-st  idea  of  what  we  mean. 
We  cannot  say  exactly  what  is  requisite  to  mako  a  government 
constitutional,  without  including  also  governments  which  we  do 
not  Intend  to  include;  and  so  of  civilized  nations;  these  tertDj 
have  neither  distinct  nor  clear  meanings. 


KNOWLEDGE  OF  TERMS.  69 

(t  is  to  be  remarked  that  no  simple  idea,  sueb  as  that  of  red 
ular,  can  be  distinct  in  tlie  meaning  here  intended,  because  no- 
bod/  can  analyze  red  color,  or  describe  to  another  person  wliat 
It  is.  A  person  who  has  been  blind  from  birth  cannot  be  made 
to  conceive  it ;  and  it  is  only  by  bringing  an  actual  red  object 
before  the  eye  that  we  can  define  its  character.  The  same  is 
generally  true  of  all  simple  sensations,  whether  tastes,  smells, 
colors,  or  sounds;  these,  then,  may  be  clearly  known,  but  not 
distinctly,  in  the  meaning  which  Leibnitz  gives  to  this  word- 


(3)  Adequate  and  Inadequate  Knowledge  Distin- 
guished.— To  explain  the  diiferencc  wliich  Leibnitz 
intended  to  denote  by  the  names  adequate  and  inade- 
quate, is  not  easy.  He  says,  *'  When  everything  Avhich 
enters  into  a  distinct  notion  is  distinctly  known,  or 
when  the  last  analysis  is  reached,  the  knowledge  is 
adequate,  of  which  I  scarcely  know  whether  a  perfect 
example  can  be  offered — the  knowledge  of  numbers, 
however,  approaches  near  to  it." 

To  have  adequate  knowledge  of  things,  then,  we 
must  not  only  distinguish  the  parts  which  make  up 
our  notion  of  a  thing,  but  the  parts  which  make  up 
those  parts.  For  instance,  we  might  be  said  to  have 
an  adequate  notion  of  a  chess-board,  because  we  know- 
it  to  be  made  up  of  64  squares,  and  we  know  each 
of  those  squares  distinctly,  because  each  is  made 
up  of  4  equal  right  lines,  joined  at  right  angles. 
Nevertheless,  we  cannot  be  said  to  have  a  distinct 
notion  of  a  straight  line,  because  we  cannot  well 
define  it,  or  resolve  it  into  anything  simpler.  To 
be  completely  adequate,  our  knowledge  ought  to  ad- 
mit of  analysis  after  analysis  ad  infinitum,  so  that 
adequate  knowledge  would  be  impossible.     But,  as  Dr 


60  TERMS. 

Thomson  remarks,  we  may  consider  any  knowledge 
adequate  which  carries  the  analysis  sufficiently  far  for 
the  purpose  in  view. 

A  mechanist,  for  instance,  has  adequate  knowledge  of  a 
.■nachine,  if  he  not  only  knows  its  several  wheels  and  parts,  but 
the  purposes,  materials,  forms,  and  actions  of  those  parts ;  pro- 
vided, again,  that  he  knows  all  the  mechanical  properties  of 
the  materials,  and  the  jjeoraetrical  properties  of  the  forms  which 
may  influence  the  working  of  the  machine.  But  he  is  not  ex» 
pected  to  go  on  still  further  and  explain  why  iron  or  wood  of  a 
particular  quality  is  strong  or  brittle,  why  oil  acts  as  a  lubricator, 
or  on  what  axioms  the  principles  of  mechanical  forces  are 
founded. 

(4)  Intuitive  and  Symbolical  Knowledge  Distin* 
guished. — Lastly,  we  must  notice  the  very  important 
distinction  of  symbolical  and  intuitive  knowledge. 
From  the  original  meaning  of  the  word,  intuitive 
would  denote  that  which  we  gain  by  seeing  (Latin, 
intuenr,  to  look  at),  and  any  knowledge  which  we  have 
directly  through  the  senses,  or  by  immediate  communi- 
cation to  the  mind,  is  called  intuitive.  Thus  we  may 
learn  intuitively  what  a  square  or  a  hexagon  is,  but 
hardly  what  a  chiliagon  or  figure  of  1000  sides  is. 

We  could  not  tell  the  difference  by  sight  of  a  figure 
of  1000  sides  and  a  figure  of  1001  sides.  Nor  can  we 
imagine  any  such  figure  completely  before  the  mind. 
It  is  known  to  us  only  by  name  or  symbolically. 
A.11  largo  numbers,  such  as  those  which  state  the 
velocity  of  light  (180,000  miles  per  second),  the  dis- 
tance of  the  sun  (91,000.000  miles),  and  the  like,  are 
iinown  to  us  only  by  symbols,  and  they  are  beyond  oui 
powers  of  imagination. 


KNOWLEDGE   OP  TERMS.  61 

In  arithmetic  and  algebra  we  are  chiefly  occupied 
urith  symbolical  knowledge  only,  since  it  is  not  neces- 
sary in  working  a  long  arithmetical  question  or  an  alge- 
braical problem  that  we  should  realize  to  ourselves  at 
each  step  the  meaning  of  the  numbers  and  symbols. 
We  learn  frem  algebra  that  if  we  multiply  together  the 
gum  and  difference  of  two  quantities  we  get  the  differ- 
ence of  the  squares  ;  as  in  symbols 

{a  +  b)  {a-b)  =  a^-Iy^: 

which  is  readily  seen  to  be  true,  as  follows 

a  -H  ft 


cfi  +  ab 

03+0  —  52. 

In  the  above  we  act  darkly  or  symbolically,  using  the 
letters  a  and  h  according  to  certain  fixed  rules,  withoui 
knowing  or  caring  what  they  mean ;  and  whatever 
meaning  we  afterwards  give  to  a  and  b  we  may  be  sure 
the  process  holds  good,  and  that  the  couclusion  is  true 
without  going  over  the  steps  again. 

But  in  geometry,  we  argue  by  intuitive  perception  of 
the  truth  of  each  step,  because  we  actually  employ  a 
representation  in  the  mind  of  the  figures  in  question, 
and  satisfy  ourselves  that  the  requisite  properties  are 
really  possessed  by  the  figures.  Thus  the  algebraical 
truth  shown  above  in  symbols  may  l)e  easily  i)roved  to 
hold  true  of  lines  and  rectangles  contained  under  those 
lines,  as  a  corollary  of  the  5th  Prop,  of  Euclid's  Second 
Book. 


fiB  TEBXB. 

3,  The    Intuitive  and  Symbolic  Methods  Com- 
pared. 

Much  might  be  said  concerning  the  comparative  ad- 
vantages of  the  intuitive  and  symbolical  methods.  The 
latter  is  usually  much  the  less  laborious,  and  gives  the 
most  widely  applicable  answers;  but  the  symbohcal 
seldom  or  never  gives  the  same  command  and  compre- 
hension of  the  subject  as  the  intuitive  method.  Hence 
the  study  of  geometry  is  always  indispensable  in  educa- 
tion, although  the  same  truths  are  often  more  readily 
proved  by  algebra.  It  is  the  peculiar  glory  of  Newton 
that  he  WJis  able  to  explain  the  motions  of  the  heavenly 
bodies  by  the  geometric  or  intuitive  method;  whereas 
the  greatest  of  his  successors,  such  as  Lagrange  or 
Laplace,  have  treated  these  motions  by  the  aid  of 
symbols. 

What  18  true  of  mathematical  subjects  may  bo  ap- 
plied to  all  kinds  of  reasoning  ;  for  words  are  symbols 
as  mucti  as  A,  B,  C,  or  x,  y,  z,  and  it  is  possible  to 
argue  with  words  without  any  consciousness  of  tneir 
meaning.  Thus  if  I  say  that  "selenium  is  a  dyad 
element,  and  a  dyad  clement  is  one  capable  of  replacing 
two  e<iuivalents  of  hydrogen,"  no  one  ignorant  of 
chemistry  will  be  able  to  attach  any  meaning  to  these 
terms,  and  yet  any  one  will  be  able  to  conclude  that 
"selenium  is  capable  of  replacing  two  equivalents  of 
hydrogen."  Such  a  person  argues  in  a  purely  symboli- 
cal manner.  Similarly,  whenever  in  common  life  wo 
use  words,  without  having  in  mind  at  the  moment  the 
full  and  precise  meanmg  of  the  words,  we  possess  sym- 
bolical  knowledge  only. 


KNOTfLEDGE  OF  TERMS.  63 

There  is  no  worse  habit  for  a  student  or  reader  to  acquire 
than  that  of  accepting  words  instead  of  a  knowledge  of  things. 
It  is  perhaps  worse  than  useless  to  read  a  work  on  natural  history 
about  Infusoria,  Foraminifera,  Rotifera  and  the  like,  if  these 
names  do  not  convey  clear  images  to  the  mind.  Nor  can  a 
student  who  has  not  witnessed  experiments,  and  examined  the 
substances  with  his  own  eyes,  derive  any  considerable  advantage 
from  works  on  chemistry  and  natural  philosophy,  where  he  will 
meet  with  hundreds  of  new  terms  wliich  would  be  to  him  mere 
empty  and  confusing  signs.  Un  this  account  we  should  lose  no 
opportunity  of  acquainting  ourselves,  by  means  of  our  senses, 
with  the  forms,  proj)ertie8  and  changes  of  things,  in  order  that 
the  language  we  employ  may,  as  far  as  possible,  be  employed 
intuitively,  and  we  may  be  saved  from  the  absurdities  and  falla- 
cies into  which  we  might  otherwise  fall.  We  should  observe,  in 
short,  the  advice  of  Bacon — Ipsis  conmescere  rebus — to  accustom 
ourselves  to  things  themselves. 

Hamilton's  Lectures  on  Logic,  Lect.  IX. 

Baynes'  Port  Royal  Logic.    Part  I,  Chap.  IX,  and  Appendix. 

Ill  this  section,  on  "The  Perfect  and  the  Im- 
perfect Knowledge  of  Terms,"  we  have  con- 
sidered :— 

1.  The  Statement  of  the  Question. 

2.  The  Scheme  of  Uistinction.s. 

3.  The  Intuitive  and   Symbolic    Methods    Com* 

pared. 


CHAPTEB    n. 

PROPOSITIONS. 

The  treatment  of  Propositions  will  involve  a  con 
sideration  of  the  following  topics  :  (1)  Tfie  Rinds 
of  Propositions;  (2)  The  Opposition  of 
Propositions ;  (3)  Conversion  and  Imme- 
diate Inference  ;  and  (4)  The  Logical  Anal' 
ysis  of  Sentences*  These  topic5s  will  be  treated  in 
separate  sections. 


SECTION    I. 

THE   KINDS  OF   PROPOSITIONS. 

1.  Meauingr  of  •*  Proposition  '*  Explained. 

A  term  standing  alone  is  not  capable  of  expressing 
trath ;  it  merely  refers  the  mind  to  some  object  or 
class  of  objects,  about  which  something  may  be  affirmed 
or  denied,  but  about  which  the  term  itself  does  not 
affirm  or  deny  anything.  "Sun,"  **air,"  ** table," 
suggest  to  every  mind  objects  of  thought,  but  we  can- 
not say  that  "sun  is  true,"  or  *'air  is  mistaken,"  or 
"table  is  false."  We  must  join  words  or  terms  into 
sentences  or  propositions  before  they  can  express  those 
reasoning  actions  of  the  mind  to  which  truth  or  falsity 
may  be  attributed.  "  The  sun  is  bright,"  **  the  air  is 
fresh,"  "  the  table  is  unsteady,"  are  statements  which 
may  be  true  or  may  be  false,  but  we  can  certainly 
entertain  the  question  of  their  truth  in  any  circum- 
stances.    Now  as  the  logical  term  was  defined  to  be 


KINDS  OF  PROPOSITIOlfS.  66 

any  combination  of  words  expressing  an  act  of  simple 
appreliension,  so  u  logical  proposition  is  any  combina- 
tion of  words  expressing  an  act  of  judgment.  The 
proposition  is,  in  short,  the  result  of  an  act  of  judg- 
ment reduced  to  the  form  of  language. 

What  the  logician  calls  a  proposition  the  grammarian  calls  a 
sentence.  But  though  every  proposition  is  a  sentence,  it  is  not 
to  be  supposed  that  every  sentence  is  a  proposition.  Tiiere  are 
in  fact  several  kinds  of  sentences  more  or  less  distinct  from  a 
proposition,  such  as  a  Sentence  Interrogative  or  Question,  a  Sen- 
tence Imperative  or  a  Command,  a  Sentence  Optative,  which  ex- 
presses a  wish,  and  an  Exclamatory  Sentence,  which  expresses 
an  emotion  of  wonder  or  surprise.  These  kinds  of  sentence 
may  possibly  be  reduced,  by  a  more  or  less  indirect  mode  of 
expression,  to  the  form  of  a  Sentence  Indicative,  which  is  the 
grammatical  name  for  a  proposition  ;  but  until  this  be  done  they 
have  no  proper  place  in  Logic,  or  at  least  no  place  which  logicians 
have  hitherto  sufficiently  explained. 

2.  Analysis  of  a  Proposition. 

The  name  proposition  is  derived  from  the  Latin 
words  pro,  before,  and  pono,  I  place,  and  means  the 
laying  or  placing  before  any  person  the  result  of  an  act 
of  judgment.  Now  every  act  of  judgment  or  compari- 
son must  involve  the  two  things  brought  into  compari- 
son, and  every  proposition  will  naturally  consist  of  three 
parts — the  two  terms,  or  names,  denoting  the  things 
compared,  and  the  copula,  or  verb,  indicating  the  con- 
nection between  them,  as  it  was  ascertained  in  the  act 
of  judgment.  Thus  the  proposition,  '*  Gold  is  a  yellow 
substance,"  expresses  an  agreement  between  gold  and 
certain  other  substances  previously  called  yellow  in  re- 
gard to  their  color.  Gold  and  yelloio  substance  are 
evidently  the  two  terms,  and  is  the  copula. 


66  PROPOSITIONS. 

It  is  always  usual  to  call  the  first  terra  of  a  proposi- 
tion the  subject,  since  it  denotes  the  underlying  matter, 
as  it  were  (Latin,  sub,  under,  and  jactum,  laid)  about 
which  soraetiiing  is  asserted.  The  second  term  is 
called  the  predicate,  which  simply  means  that  which  is 
affirmed  or  asserted. 

This  name  is  derived  from  tlie  Latin  pradlcare,  to  assert, 
whence  comes  the  French  name  predicuteur.  corrupted  into  our 
preacher.  This  Latin  verb  is  not  to  be  confused  with  the  some- 
what similar  one  predicere,  which  has  the  entirely  different 
meaning  to  predict  or  foretell.  I  much  suspect  that  newspaper 
writers  and  others,  who  pedantically  use  the  verb  "  to  predicate," 
sometimes  fall  into  this  confusion,  and  really  mean  to  predict,  but 
it  is  in  any  case  desirable  that  a  purely  technical  term  like  predi- 
cate should  not  be  needlessly  introduced  into  common  language, 
when  there  are  so  many  other  good  words  which  raigiit  be  used. 
This  and  all  other  technical  scientific  terms  should  be  kept  to 
their  projjer  scientific  use,  and  the  neglect  of  this  rule  injures  at 
once  the  lanf^uage  of  common  life  and  the  language  of  science. 

3.  Categorical  and  Conditional  Propositions. 

Propositions  are  distinguished  into  two  kinds,  accord- 
ing a.s  they  make  a  statement  conditionally  or  uncondi- 
tionally. Thus  the  proposition,  "If  metals  are  heated 
they  are  softened,"  is  conditional,  since  it  does  not 
make  an  assertion  concerning  metals  generally,  but 
only  in  the  circumstances  when  they  become  heated. 
Any  circumstance  which  must  be  granted  or  supposed 
before  the  assertion  becomes  applicable  is  a  condition. 
Conditional  propositions  are  of  tvvo  kinds,  Hypothetical 
and  Disjunctive,  but  their  consideration  will  be  best 
deferred  to  a  subsequent  chapter.  Unconditional  prop- 
ositions are  those  with  which  we  shall  for  some  time 


KINDS   OF   PROPOSITIONS.  6? 

be  solely  concerned,  and  these  are  usually  called  Cate- 
gorical propositions,  from  the  Greek  verb  xarT/yopt-a 
{kategoreo,  to  assert  or  affirm). 

The  following  diagram  will  conveniently  represent 
the  classification  of  sentences  and  propositions  as  far  as 
we  have  yet  proceeded : — 

„  f  Indicative  =  Prop,  -i  r^^3!lt^^\!i  Hypothetical. 
I     Interrogative  '  ^^^^^^^^"^^1  Disjunctive. 

I  •  Imperative 
H     Optative 
"^  I  Exclamatory 


4.  The  Quality  and  Quantity  of  Propositions. 

It  is  now  necessary  to  consider  carefully  the  several 
kinds  of  categorical  proi)ositions.  They  are  classified 
according  to  quality  and  according  to  quantity.  As 
regards  quality  they  are  either  affirmative  or  negative  ; 
as  regards  quantity  they  are  either  universal  or  par- 
ticular. 

An  affirmative  proposition  is  one  which  asserts  a  cer- 
tain agreement  between  the  subject  and  predicate,  so 
that  the  qualities  or  attributes  of  the  predicate  belong 
to  the  subject.  The  proposition,  "gold  is  a  yellow 
substance,"  states  such  an  agreement  of  gold  with  other 
yellow  substances,  that  w^e  know  it  to  have  the  color 
yellow,  as  well  as  whatever  qualities  are  implied  in  the 
name  substance.  A  negative  proposition,  on  the  other 
hand,  asserts  a  difference  or  discrepancy,  so  that  some 
at  least  of  the  qualities  of  the  predicate  do  not  belong 
to  the  subject.  "Gold  is  not  easily  fusible"  denies  that 
the  quality  of  being  easily  fused  belongs  to  gold. 

Propositions  are  again  dividoJ  according  to  quantity 


68  PROPOSITIONS. 

into  universal  and  particular  propositions.  If  the  prop- 
osition affirms  the  predicate  to  belong  to  the  whole  of 
the  subject,  it  is  an  universal  proposition,  as  in  the  ex- 
ample "all  metals  are  elements,"  which  affirms  that 
the  quality  of  being  undecomposable  or  of  being  simple 
in  nature  is  true  of  all  metals.  But  if  we  say  "some 
metals  are  brittle,"  the  quality  of  brittleness  is  affirmed 
only  of  some  indefinite  portion  of  the  metals,  and  there 
is  nothing  in  the  proposition  to  make  us  sure  that  any 
certain  metal  is  brittle.    This  is  a  particular  proposition. 

The  name  particular  being  derived  from  the  diminutive  of  the 
Latin  para  would  naturally  signify  a  small  part,  but  in  logic  it 
must  be  carefully  interpreted  as  signifying  any  part,  from  the 
smallest  fraction  up  to  nearly  tbe  whole.  Particular  propositions 
do  not  include  cases  where  a  predicate  is  affirmed  of  the  whole  or 
of  none  of  the  subject,  but  they  include  any  between  these 
limits.  We  may  accordingly  count  among  particular  proposi- 
tions all  such  as  the  following : — 

A  very  few  metals  are  less  dense  than  water. 

Most  elements  are  metals. 

Many  of  the  planets  are  comparatively  small  bodies. 

Not  a  few  distinguished  men  have  had  distinguished  sons. 

The  reader  must  carefully  notice  the  somewhat  subtle  point 
ex])lained  further  on,  that  the  particular  proposition  though  as- 
serting the  predicate  only  of  a  part  of  the  subject,  does  not  deny 
it  to  be  true  of  the  whole. 

5.  Aristotle^s  View  of  Quantity. 

Aristotle  considered  that  there  were  altogether  four 
kinds  of  proposition  as  regards  quantity,  namely — 

(  Universal. 
_  Particular. 

Proposition  ^  j^i^g^i^r. 

Indefinite. 


KINDS   OF  PROPOSITIONS.  69 

The  singular  proposition  is  one  which  has  a  singular 
term  for  its  subject,  as  in — 

Socrates  was  very  wise. 
London  is  a  vast  city. 

But  we  may  fairly  consider  that  a  singular  proposi- 
tion is  an  universal  one;  for  it  clearly  refers  to  the 
whole  of  the  subject,  which  in  this  case  is  a  single 
individual  thing. 

Indefinite  or  indesignate  propositions  are  those  which 
are  devoid  of  any  mark  of  quantity  whatever,  so  that 
the  form  of  words  gives  us  no  mode  of  judging  whether 
the  predicate  is  applicable  to  the  whole  or  only  part  of 
the  subject.  Metals  are  useful,  Comets  are  subject  to 
the  law  of  gravitation,  are  indefinite  propositions.  In 
reality,  however,  such  propositions  have  no  distinct 
place  in  logic  at  all,  and  the  logician  cannot  properly 
treat  them  until  the  true  and  precise  meaning  is  made 
apparent. 

The  predicate  must  be  true  either  of  the  whole  or  of  part  of 
the  subject,  so  that  the  proposition,  as  it  stands,  is  clearly  incom 
plete  ;  but  if  we  attempt  to  remedy  this  and  supply  the  marks  of 
quantity,  we  overstep  the  proper  boundaries  of  logic  and  assume 
ourselves  to  be  acquainted  with  the  subject  matter  or  science  of 
which  the  proposition  treats.  We  may  safely  take  the  preceding 
examples  to  mean  "some  metals  are  useful  "  and  "  nil  comets  are 
subject  to  the  law  of  gravitation,"  but  not  on  logical  grounds. 
Hence  we  may  strike  out  of  logic  altogether  the  class  of  indefinite 
propositions,  on  the  understandiu'^  that  tliey  must  be  rendered 
definite  before  we  treat  them.  In  the  following  sections  we  sliall 
frequently  use  propositions  in  tlie  indefinite  fonnas  examples,  on 
the  understanding  that  where  no  sign  of  quantity  apix^ars,  the 
universal  quantity  is  to  be  assumed.  It  is  probable  that  wherever 
a  terra  is  used  alone,  it  ought  to  bo  interpreted  as  meaning  the 
whole  of  its  class.     But  however  this  may  be,  we  need  not  recojf 


70  PROPOSITIONS. 

nize  the  indefinite  proposition  as  a  distinct  kind ;  and  singulai 
propositions  liaving  been  resolved  into  universais,  there  remain 
onlj  the  two  kinds,  Universal  and  Particular. 

6.  Names  of  the  Four  Propositions. 

Remembering  now  tnat  there  are  two  kinds  of  prop- 
osition as  regards  quality,  and  two  as  regards  quantity, 
we  shall  be  able  to  form  altogether  four  varieties, 
thus  : 


Proposition 


f  Universal  j^®'""^.^*^^^  ^ 

( Negative  E 

Particular  i  Affirmative  I 

i-articuiar  |  j^ggj^ti^,.  q 


The  vowel  letters  placed  at  the  rigiit  Hand  are  sym- 
bols or  abbreviated  names,  whicli  are  always  used  to 
denote  the  four  kinds  of  proposition  ;  and  there  will  be 
no  difficulty  in  remembering  their  meaning:  if  we  ob- 
serve A  and  I  occur  in  the  Latin  verb  affirmo,  I  affirm, 
and  E  and  0  in  nego,  I  deny. 

There  will  generally  be  no  difflculty  in  referring  to  its  proper 
class  any  proposition  tliat  we  meet  witli  in  writings.  The  mark 
of  universality  usually  consists  of  some  adjecti>'e  of  quantity, 
such  as  nil,  etery,  each,  any,  the  wfiole ;  but  whenever  the  predi- 
cate is  clearly  intended  to  apply  to  the  whole  of  the  subject  wo 
may  treat  the  proposition  as  universal.  The  signs  of  a  particu- 
lar proposition  are  the  adjectives  of  quantity,  8ome,  certain;  a  few, 
many,  moat,  or  such  others  as  dearly  indicate  part  at  least. 

The  negative  proposition  is  known  by  the  advi-riiial  particle 
not  being  joined  to  the  copula  ;  but  in  the  proposition  E,  that  is 
the  universal  negative,  wo  frequently  use  the  particle  no  or  none 
prefixed  to  the  subject.  Thus,  "  no  metals  are  compound,"  "none 
of  tlu'  ancients  were  acquainted  with  the  laws  of  motion,"  are 
familiar  forms  of  the  universal  negative. 


KIKDS   OF   PROPOSITIONS.  71 

The  student  must  always  be  prepared  too  to  meet  with  miB- 
leading  or  ambiguous  forms  of  expression.  Thus  the  proposition, 
"all  the  metals  are  not  denser  than  water,"  might  be  taken  as  E 
or  O,  according  as  we  interpret  it  to  mean  "  no  metals  are  denser 
than  water,"  or  "  not  all  the  metals,"  etc.,  the  last  of  course  being 
the  true  sense.  The  little  adjective /gw  is  very  subject  tea  subtle 
ambiguity  of  this  kind ;  for  if  I  say  "■few  hooka  are  at  once 
learned  and  amusing."  I  may  fairly  be  taken  to  assert  that  a  few 
books  certainly  are  so,  but  what  I  really  mean  to  draw  attention 
to  is  my  belief  that  "  the  greater  number  of  books  are  not  at  once 
learned  and  amusing."  A  proposition  of  this  kind  is  generally 
to  be  classed  rather  as  O  than  I.  The  word  some  is  subject  to 
an  exactly  similar  ambiguity  between  some  but  not  all,  and  some 
at  least,  it  may  be  all ;  the  latter  appears  to  be  the  correct  inter- 
pretation, as  shown  in  the  following  section  (p.  77). 

As  propositions  are  met  with  in  ordinary  language  they  are 
subject  to  various  inversions  and  changes  of  the  simple  logical 
form. 

(I)  It  is  not  uncommon,  especially  in  poetry,  to  find  the  predi- 
cate placed  first,  for  the  sake  of  emphasis  or  variety  ;  as  in 
"  Blessed  are  the  merciful ; "  "  Comes  something  down  with  even- 
tide ;"  "  Great  is  Diana  of  the  Ephesians."  There  is  usually  no 
diflBculty  in  detecting  such  an  inversion  of  t!ie  terms,  and  the 
sentence  must  then  be  reduced  to  the  regular  order  before  being 
treated  in  logic. 

(3)  The  subject  may  sometimes  be  mistaken  for  the  predicate 
when  it  is  described  a  relative  clause,  standing  at  the  end  of  the 
sentence,  as  in  "  no  one  is  free  who  is  enslaved  by  his  appetites." 
Here  free  is  evidently  the  predicate,  although  it  stands  in  the 
middle  of  the  sentence,  and  "  one  who  is  enslaved  by  his  appe- 
tites "  is  the  real  subject.  This  proposition  is  evidently  of  the 
form  E. 

7.  Variations  from  the  Logical  Form. 

Propositions  are  also  expressed  in  various  modes 
differing  from  the  simple  logical  order,  and  some  of  the 
different  kinds  which  arise  must  be  noticed. 


72  PROPOSITIONS. 

(1)  Exclusive  propositions  contain  some  words,  such 
as  only,  alone,  nune  but,  which  limit  the  predicate  to 
the  subject  Thus,  in  "elements  alone  are  metals,"  we 
are  informed  that  the  predicate  "metal"  cannot  be 
applied  to  anything  except  "elements,"  but  we  are  not 
to  understand  that  "all  elements  are  metals."  The 
same  meaning  is  expressed  by  "  none  but  elements  are 
metals;"  or,  again,  by  "all  that  arc  not  elements  are 
not  metals;"  and  this  wc  jhall  sec  in  the  next  lesson  is 
really  equivalent  to  "all  metals  are  elements."  Argu- 
ments which  appear  fallacious  at  first  sight  will  often 
be  found  correct  when  they  contain  exclusive  proposi- 
tions and  these  are  properly  interpreted. 

(2)  Exceptive  propositions  affirm  a  predicate  of  all 
the  subject  with  the  exception  of  certain  defined  cases, 
to  which,  as  is  implied,  the  predicate  does  not  belong. 
Thus,  "  all  the  planets,  except  Venus  and  Mercury,  are 
beyond  the  earth's  orbit,"  is  a  proposition  evidently 
equivalent  to  two,  viz.,  that  Venus  and  Mercury  are 
not  beyond  the  earth's  orbit,  but  that  the  rest  are.  If 
the  exceptions  are  not  actually  specified  by  name  an 
exceptive  proposition  must  often  be  treated  as  a  partic- 
ular one.  For  if  I  say  "all  the  planets  in  our  system 
except  one  agree  with  Bode's  law,"  and  do  not  give  the 
name  of  that  one  exception,  the  reader  cannot,  on  the 
ground  of  the  proposition,  assert  of  any  planet  positively 
that  it  does  agree  with  Bode's  law. 

(3)  Explicative  op  essential  propositions  are  so  called 
because  they  merely  affirm  of  their  subject  a  predicate 
which  is  known  to  belong  to  it  by  all  who  can  define 
the  subject.  Such  propositions  merely  unfold  what  is 
already  contained  in  the  subject     "A  parallelogram 


KINDS   OF   PROPOSITIONS.  73 

has  four  sides  and  four  angles,"  is  an  explicative 
or  essential  proposition.  "  London,  which  is  the  capi- 
tal of  England,  is  the  largest  city  of  Europe,"  contains 
two  propositions ;  of  which  one  merely  directs  our  at- 
tention to  a  fact  which  all  may  be  supposed  to  know, 
viz.,  that  London  is  the  capital  of  England. 

(4)  Ampliative  propositions,  ^u  the  other  hand,  join 
a  new  predicate  to  the  subject.  Thus  to  those  who  do 
not  know  the  comparative  sizes  of  cities  in  Europe,  the 
last  example  contains  an  ampliative  proposition.  The 
gi'eater  number  of  propositions  are  of  this  kind. 

(5)  Tautologous  or  Truistic  propositions  are  those 
which  merely  affirm  the  subject  of  itself,  and  give  no 
information  whatever  ;  as  in,  "whatever  is,  is;"  "what 
I  have  written,  1  have  written." 

It  is  no  part  of  formal  Logic  to  teach  us  how  to  interpret  the 
meanings  of  sentences  as  we  meet  them  in  writings ;  this  is 
rather  the  work  of  the  grammarian  and  philologist.  Logic  treats 
of  the  relations  of  the  different  propositions,  and  the  inferences 
which  can  be  drawn  from  them  ;  but  it  is  nevertheless  desirable 
that  the  reader  should  acquire  some  familiarity  witli  the  real 
logical  meaning  of  conventional  or  peculiar  forms  of  expression, 
and  a  number  of  examples  will  be  found  at  the  end  of  the  book, 
>vhich  the  learner  is  requested  to  classify  and  treat  as  directed. 

8.  The  Modality  of  Propositions. 

In  addition  to  the  distinctions  already  noticed  it  has 
long  been  usual  to  distingiiish  propositions  as  they  are 
pure  or  modal.  The  pure  proposition  simply  asserts 
that  the  predicate  does  or  does  not  belong  to  the  sub- 
ject, while  the  modal  proposition  states  this  cum  mndo. 
or  with  an  intimation  of  the  mode  or  manner  in  which 
the  predicate  belongs  to  the  subject.     The  presence  of 


74  PROPOSITIONS. 

any  adverb  of  time,  place,  manner,  degree,  etc.,  or  any 
expression  equivulent  to  an  adverb,  confers  modality  on 
a  proposition.  "  Error  is  always  in  haste  ; "  "justice  is 
ever  equal;  "a  perfect  man  ought  always  to  be  con- 
quering himself,"  are  examples  of  modal  propositions 
in  this  acceptation  of  the  name. 

Other  logicians,  however,  have  adopted  a  different  view,  and 
treat  modality  as  consisting  in  the  degree  of  certainty  or  pro- 
bability vvith  which  a  judgment  is  made  and  asserted.  Thus, 
we  may  say,  "an  equilateral  triangle  is  necessarily  oqumngular ;" 
"  men  are  generally  trustworthy;  "  "  a  falling  barometer  probably 
indicates  a  coming  storm ;  "  "Aristotle's  lost  treatises  may  possibly 
be  recovered  ;  "  and  all  these  assertions  are  made  with  a  different 
degree  of  certainty  or  modality.  Dr.  Thomson  is  no  doubt  right 
in  holding  that  the  modality  does  not  affect  the  copula  of  the 
proposition,  and  the  subject  could  only  be  properly  treated  in  a 
work  on  Probable  Reasoning, 

Many  logicians  have  also  divided  propositions  according  as  they 
are  true  or  false,  and  it  might  well  seem  to  be  a  distinction  of 
importance.  Nevertheless,  it  is  wholly  beyond  the  province  of 
the  logician  to  consider  whether  a  proposition  is  true  or  not 
in  itself;  all  that  he  has  to  determine  is  the  oom!)arative  truth 
of  ])ropo8itions — that  is,  whether  one  proposition  is  true  when 
another  is.  Strictly  speakinp,  logic  has  nothing  to  do  with  a 
proposition  by  itself;  it  i.s  only  in  converting  or  transmuting 
certain  propositions  into  certain  others  that  the  work  of  reason- 
ing consists,  and  the  truth  of  the  conclusion  is  only  so  far  in 
question  as  it  follows  from  the  truMi  of  what  we  shall  call  the 
premises.  It  is  the  duty  of  the  special  sciences  each  in  its  own 
sphere  to  determine  what  are  true  propositions  and  what  are 
false,  and  logic  would  be  but  another  name  for  the  whole  of 
knowledge  could  it  take  this  duty  on  itself. 

See  Mr.  Mill's  System  of  Logic,  Book  I,  Chap.  IV,  which  gener- 
ally ftirrees  witli  what  U  given  alwve.  ('Iiapters  V  and  VI 
contain  Mr.  Mill's  views  on  the  Nature  and  Import  of  Prop- 


OPPOSITION   OF   PROPOSITIONS   EXPLAINED.  75 

ositionR,  which  subject  may  be  further  studied  in  Mr.  Mill's 
Examination  of  Sir  W.  Hamilton's  Philosophy,  Ciiap.  XVIII; 
Hamilton's  L  ctures  on  Logic,  No.  XIII ;  and  Mansel's  Pro- 
legomena Logica,  Chap.  II ;  but  the  subject  is  too  metaphy- 
sical in  character  to  be  treated  in  this  work. 

In  this  Section,  on  "Tlie  Kinds  of  Propositions,** 
we  have  considered:— 

1.  The  Meaning  of  the  Word  "  Proposition." 

2.  The  Amilysis  of  a  Proposition. 

3.  The  Cateijo rival  and  Conditional  Propositions, 

4.  The  Quality  and  Quantity  of  Propositions, 
6.  Aristotle\s  View  of  Quantity, 

6.  Names  of  the  Four  Propositions. 

7.  Variations  from  the  Loyical  Form, 

8.  The  Modality  of  Propositions. 


SECTION    IL 

THE   OPPOSITION    OF    PROPOSITIONS. 

1.  The  Four  Propositions  Explained. 

We  have  ascertained  that  four  distinct  kinds  of  prop- 
ositions are  recognized  by  logicians, — the  Universal 
affirmative,  the  Particular  affirmative,  the  Universal 
negative,  and  the  Particular  negative,  commonly  indi- 
cated by  the  symbols  A,  E,  I,  O.  It  is  now  desirable  to 
compare  together  somewhat  minutely  the  meaning  and 
use  of  propositions  of  these  various  kinds,  so  that  we 
may  clearly  learn  how  the  truth  of  one  will  affect  the 
truth  of  others,  or  how  the  same  truth  may  be  thrown 
into  various  forms  of  expression. 


76  PROPOSITIONS. 

(1)  The  universal  affirmative  proposition  A  expresses 
the  fact  that  the  thing  or  chiss  of  tilings  denoted  by  the 
subject  is  included  in,  and  forms  part  of  the  class  of 
things  denoted  by  the  predicate.  Thus  "all  metals  are 
elements  "  means  that  metals  form  a  part  of  the  class  of 
elements,  but  not  the  whole.  As  there  are  altogether  63 
known  elements,  of  which  48  are  metals,  we  cannot  say 
that  all  elements  are  metals.  The  proposition  itself 
does  not  tell  us  anything  about  elements  in  general ;  it 
is  not,  in  fact,  concerned  with  elements,  metals  being 
the  subject  about  which  it  gives  us  information.  This 
is  best  indicated  by  a  kind  of  diagram,  first  used  by  the 
celebrated  mathematician  Euler,  in  his  letters  to  a 
German  princess.     In  Fig.  1,  the  metals  are  supposed 

Fig.  1. 


t»  be  enclosed  in  the  small  circle  somewhat  as  sheep 
might  be  in  a  pinfold,  this  circle  containing  all  the 
metals  and  nothing  else.  The  greater  circle  is  sup- 
posed to  contain  in  a  similar  manner  all  the  elements 
and  nothing  else.  Now  as  the  small  circle  is  wholly 
within  the  larger  one,  it  follows  that  all  the  metals 
must  be  counted  as  elements,  but  of  the  part  of  the 
elements  outside  the  circle  of  metals  we  know  nothing 
from  tho  proposition. 

(2)  The  particular  affirmative   proposition  I  exactl) 


OPPOSITION   OF  PROPOSITIONS   EXPLAINED.  77 

resembles  A  in  meaning,  except  tliut  only  part  of  the 
subject  is  brought  into  question.  When  I  say  that 
"some  metals  are  brittle,"  I  mean  that  of  a  collection  of 
all  the  different  metals  a  few  at  least  might  be  picked 
out  which  would  be  found  to  be  brittle  ;  but  the  word 
some  is  exceedingly  indefinite,  showing  neither  the 
exact  number  of  brittle  metals,  nor  how  we  are  to 
know  them  from  the  others,  unless  indeed  by  trying 
whether  they  are  brittle.  This  proposition  will  be 
properly  represented  in  Euler's  mode  by  two  intersect- 
ing circles,  one  supposed  to  enclose  all  metals,  and  the 
other  all  brittle  substances.     The  mere  fact  of  the  two 

Fig.  2. 


circles  intersecting  proves  that  some  part  of  one  class 
must  coincide  with  some  part  of  the  other  class,  which 
is  what  the  proposition  is  intended  to  express.  Con- 
cerning the  portions  of  the  circles  which  do  not  overlap, 
the  proposition  tells  us  nothing. 

(3)  The  universal  negative  proposition  E  denies  the 
existence  of  any  agreement  or  coincidence  between  the 
subject  and  predicate.  Thus  from  "  no  metals  are  com- 
pound substances,"  we  learn  that  no  metal  is  to  be 
found  among  compound  substances,  and  it  follows 
necessarily  that  no  compound  substance  can  be  found 
among  the  metals.     For  were  there  a  compound  sub- 


78  PROPOSITIONS. 

Stance  among  the  metals,  there  would  evidently  be  one 
metal  at  least  among  the  compound  substances.  Thie 
entire  separation  in  thought  of  the  two  classes  is  well 
shown  in  Euler's  method  by  two  disconnected  circles. 

Fia.  8. 


(4)  The  particular  negative  proposition  O  excludes  a 
part  of  the  subject  from  tbe  predicate.  Wben  I  say 
some  metals  are  not  brittle,  I  intentionally  refer  only  to 
a  part  of  the  metals,  and  exclude  them  from  the  class 
of  brittle  substances ;  bnt  I  cannot  help  at  the  same 
time  referring  to  the  whole  of  the  brittle  substances. 
If  the  metals  in  question  coincided  with  any  part  of 
the  brittle  substances  they  could  not  be  said  to  be 
excluded  from  the  class.  To  exclude  a  thing  from  any 
space,  as  from  a  particular  chamber  of  a  house,  it  must 
not  merely  be  removed  from  some  part,  but  from  any 
part,  or  from  the  whole  of  that  space  or  chamber. 
Euler's  tliagram  for  this  proposition  may  be  constructed 
in  the  same  manner  as  for  the  proposition  I  as  follows* 

Fig.  4. 


It  is  apparent  that  though  part  of  the  metals  fall  inte 


OPPOSITION  OF   PEOPOSITIONS   EX  PLAINED.  79 

the  circle  of  brittle  substances,  yet  the  remaining  por- 
tion are  excluded  from  any  part  of  the  predicate. 

2.  The  Distribution  of  Terms. 

The  learner  will  easily  see  that  the  proposition  E  is 
distinguished  from  A  and  I,  by  the  fact  that  it  gives  us 
some  information  concerning  the  ivhole  of  the  predicate, 
because  we  learn  that  none  of  the  objects  included  in 
the  predicate  can  be  found  among  those  included  in 
the  subject.  The  affirmative  propositions,  on  the  other 
hand,  warranted  us  in  holdmg  that  the  objects  denoted 
by  tiie  subject,  or  some  particular  part  of  them,  were 
included  in  the  predicate,  but  tliey  give  us  no  luarrant 
for  saying  that  any  specified  part  of  the  predicate  is  in 
the  subject.  Because  we  merely  know  that  a  substance 
is  an  element,  we  do  not  learn  from  the  proposition 
**all  metals  are  elements"  whether  it  is  metal  or  not. 
And  from  the  proposition  "  some  metals  are  brittle,"  we 
certainly  cannot  ascertain  whether  any  })articular  brittk 
substance  is  a  metal.  We  must  seek  the  information 
from  other  sources.  But  from  "  no  metals  are  com- 
pounds" we  learn  of  any  compound  substance  that  it 
is  not  a  metal,  as  well  as  of  a  metal  that  it  is  not  a 
compound  substance.  The  particular  negative  O  dis- 
tributes its  predicate,  but  not  its  subject,  for  in  saying 
some  metals  are  not  brittle,  I  exclude  some  metals  from 
the  wJiole  class  of  brittle  substances. 

The  important  difference  above  explained  is  expressed 
in  technical  language  by  saying  that  the  proposition  E 
distributes  its  predicate,  whereas  the  affirmative  proposi- 
tions A  and  I  do  not  distrihite  their  predicates.  By 
distribution  of  a  term  is  simply  meant  taking  it  univer- 


80 


PROPOSinOKS. 


sally,  or  referring  to  all  parts  of  it ;  and  as  the  validity 
of  any  argument  or  syllogism  will  usually  depend  upon 
the  sufficient  distribution  of  the  terms  occurring  in  it, 
too  much  attention  cannot  be  paid  to  this  point. 

Judging  from  the  examples  we  have  had,  it  will  be 
seen  that  the  universal  affirmative  distributes  its  sub- 
ject, but  not  its  predicate;  for  it  gives  us  some  infor- 
mation concerning  all  metals,  but  not  all  elements.  The 
particular  affirmative  distributes  neither  subject  nor 
predicate  ;  for  we  do  not  learn  anything  from  our  ex- 
ample concerning  all  metals  nor  concerning  all  brittle 
substances.  The  universal  negative  distributes  both 
subject  and  predicate,  for  we  learn  something  of  all 
metals  and  also  of  all  compound  substaiices.  The  par- 
ticular negative  distributes  its  predicate,  but  not  its  sub- 
ject, for  it  excludes  the  subject  from  the  whole  of  the 
predicate. 


8.  Table  of  Results^ 

We  may  state  the  results  at  which  we  have  now 


arrived  in  the  following  form : — 


o  i 


Universal 


j  Affirmative  A. 
j  Negative      E. 


Subject. 

Dietribiited. 
Distributed. 


Predicate. 

Undistributed 
Distributed. 


D    ..     ,       S  Affirmative  I. 
Particular    j  Negative      0. 


Undistributed.    Undistributed. 
Undistributed.    Distributed. 


4.  Relations  of  the  Four  Propositions. 

We  shall  now  discover  with  great  ease  the  relations 
of  the  four  pro)>osition8,  each  to  each,  that  is  to  say, 
the  way  in  which  they  are  opposed  to  each  other.  It 
ifi  obvious  that  the  truth  of  one  proposition  interferes 


OPPOSITION  OF  PROPOSITIONS  EXPLAINED.         81 

more  or  less  completely  with  the  truth  of  anothei 
proposition  having  the  same  subject  and  predicate.  If 
"all  metals  are  elements,"  it  is  impossible  that  '^ some 
metals  are  not  elements,"  and  still  more  palpably  im- 
possible, so  to  say,  that  "  no  metals  should  be  elemente." 
The  proposition  A,  then,  is  inconsistent  with  both  E  and 
0 ;  and,  vice  versa,  E  and  0  are  inconsistent  with  A. 
Similarly,  E  is  inconsistent  with  A  and  I.  But  this  im- 
portant difference  must  be  noted,  that  if  A  be  false,  O 
is  necessarily  true,  but  E  may  or  may  not  be  true.  If 
it  is  not  true  that  "all  men  are  sincere,"  it  follows 
that  "some  men  are  not  sincere,"  but  it  does  not  in 
the  least  follow  that  "no  men  are  sincere."  This  dif- 
ference is  expressed  by  saying  that  A  and  0  are  contra- 
dictory propositions,  whereas  A  and  E  arc  called  con- 
trary propositions.  It  is  plain  that  A  and  E,  as  in  "al! 
men  are  sincere"  and  "no  men  are  sincere,'"  represent 
the  utmost  possible  contrariety  of  circumstances.  In 
order  to  prove  the  falsity  of  A,  it  is  sufficient  to  estab- 
lish the  truth  of  0,  and  it  is  superfluous,  even  if  pos- 
sible, to  prove  E;  similarly  E  is  disproved  by  proving  I, 
and  it  is  superfluous  to  prove  A.  Any  person  who 
asserts  a  universal  proposition,  either  A  or  E,  lays  him- 
self under  the  necessity  of  explaining  away  or  disprov- 
ing every  single  exception  brought  against  it. 

An  opponent  may  always  restrict  himself  to  the  much  easier 
task  of  finding  instances  which  apparently  or  truly  contradict  the 
universality  of  the  statement.  l:ut  if  he  takes  upon  himself  to 
affirm  the  direct  contrary,  he  is  himself  open  to  easy  attack. 
Were  it  to  be  asserted,  for  instance,  that  "All  Christians  are 
more  moral  than  Pagans,"  it  would  be  easy  to  adduce  examples 
showing  that  "  Some  Christians  are  not  more  moral  than 
Pftgans,"  but  it  would  be  absurd  to  suppose  that  it  would  bt 


SI  PROPOSITIONa 

necessary  to  go  to  the  contrary  extreme,  and  show  that  "N» 
Christians  are  more  moral  than  Pagans."  In  short  A  is  suffi- 
ciently and  best  disproved  by  0,  and  E  by  i.  It  will  be  easily 
apparent  that,  vice  versa,  0  is  disproved  by  A,  and  I  by  E  ;  nor  is 
there,  indeed,  any  other  mode  at  all  of  disproving  these  particu- 
lar propositions. 


When  we  compare  together  the  propositions  I  and  0 
we  find  that  they  are  in  a  certain  sense  contrary  in 
nature,  one  being  affirmative  and  the  other  negative, 
but  that  they  are  still  consistent  with  each  other.  It  is 
true  both  that  "Some  metals  are  brittle,"  for  instance 
Antimony,  Bismuth  and  Arsenic ;  but  it  is  also  true 
that  "Some  metals  are  not  bnttle."  And  the  reader 
will  observe  that  when  I  affirm  "Some  metals  are 
elements,"  there  is  nothing  in  this  to  prevent  the  truth 
of  "Some  metals  are  not  elements,"  although  on  other 
grounds  we  know  that  this  is  not  true.  The  proposi- 
tions I  and  O  are  called  subcontraries  each  of  the  other, 
the  name  connoting  a  less  degree  of  contrariety  than 
exists  between  A  and  E. 

As  regards  the  relation  of  A  to  I  and  E  to  0,  it  is 
plain  that  the  truth  of  the  universal  includes  and 
necessitates  the  truth  of  the  particular.  What  may  be 
affirmed  or  denied  of  all  parts  of  a  class  may  certainly 
be  affirmed  or  denied  similarly  of  some  part  of  the 
class.  From  the  truth  of  the  particular  we  have  no 
right  to  infer  either  the  truth  or  falsity  of  the  universal 
of  the  same  fjuality.  These  pairs  of  propositions  are 
called  subalterns,  i.  e.,  ono.  under  the  other  (Latin  siih 
under,  and  alfer  the  oth. .  of  two),  or  we  may  say  more 
exactly  that  I  and  0  are  icspectively  the  suhaUernateS 
of  A  and  E,  each  of  which  is  a  suhalternans. 


OPPOSITION   OF   PB0P0SITI0N8   EXPLAINED. 


83 


5.  The  Scheme  of  Opposition. 

The  relations  of  the  propositions  just  described  are 
all  clearly  shown  in  the  following  scheme: 

A Contraries E 


03 

0 


I 


I 


X/-^ 

{'5'     ^^n 


^'    '°% 


0° 


.  Subcontraries , 


08 
OS 


6.  The  Laws  of  Opposition. 

It  is  so  highly  important  to  apprehend  completely 
and  readily  the  consistency  or  opposition  of  proposi- 
tions, that  I  will  put  the  matter  in  another  form.  Tak- 
ing any  two  propositions  having  the  same  subject  and 
predicate,  they  must  come  under  one  of  the  following 
statements : 

1.  Of  contradictory  propositions,  one  must  be  true 
and  one  false. 

3.  Of  contrary  propositions,  both  cannot  be  trae. 
and  both  may  be  false. 

3.  Of  subcontrary  propositions,  one  only  can  be  false., 
and  both  may  be  true. 

4.  Of  subalterns,  the  particular  is  true  if  the  univer- 
sal be  true  ;  but  the  universal  may  or  may  not  be  true 
when  the  particular  is  true. 


M  PBOPOsmoHa 

7>  The  Conditions  of  Opposition. 

1  put  the  same  matter  iu  yet  another  form  in  the 
following  table,  which  shows  how  the  truth  of  each  oi 
A,  E,  I,  and  0,  affects  the  truth  of  each  of  the  others. 


A 

E 

1 

0 

is 

is 

is 

is 

If  A  be  true 

true 

false 

true 

false. 

((  C    l(       it 

false 

true 

false 

true. 

u  1       «       (( 

doubtful 

false 

true 

doubtfuL 

tt  Q    «       « 

false 

doubtful  doubtful 

true. 

It  will  be  evident  that  from  the  affirmation  of  uni- 
versals  more  information  is  derived  than  from  the 
affirmation  of  particulars.  It  follows  that  more  infor- 
mation can  be  derived  from  the  denial  of  particulars 
than  from  the  denial  of  universals,  that  is  to  say,  there 
are  less  cases  left  doubtful,  as  in  the  above  table. 

The  learner  may  well  be  cautioned,  however,  af^inst  an  am- 
biguity which  has  misled  some  even  of  the  most  eminent  lo- 
gicians. In  particular  projKtsitions  the  adjective  some  is  to  be 
carefully  interpreted  as  some,  and  there  may  or  may  not  be  more 
or  all.  Were  we  to  interpret  it  ns  some,  not  more  nor  all,  then  it 
would  really  give  to  tlie  proposition  the  force  of  I  and  0  com- 
bined. If  I  pay  "  some  men  are  sincere,"  I  must  not  be  taken  as 
implying  that  "some  men  are  not  sincere;"  I  must  be  under- 
stood to  predicate  sincerity  of  some  men,  leaving  the  character  ol 
the  remain  ler  wholly  unaffected.  It  follows  from  this  that, 
when  I  deny  the  truth  of  a  particular,  I  must  not  be  understood 
a-s  implying  tlie  trutli  of  the  universal  of  the  same  quality.  To 
deny  the  truth  of  *•  some  men  are  mortal "  might  seem  very 
natural,  on  t!ie  ground  tliat  not  some  but  all  men  are  mortal  ;  but 
then  the  profwsition  denied  would  really  be  some  men  are  not 
mortal,  L  ••.  0  not  I.     Hence  when  I  deny  that  "some  men  art 


OPPOSITIOir  TO  PBOPOSITIOira  EXPLAimtD.         86 

tmmortal "  I  mean  that  "  no  men  are  immortal ; "  and  when  I 
deny  that  "  some  men  are  not  mortal,"  I  mean  that  "  all  men  are 
mortal" 

8.  The  Matter  of  Propositions. 

It  has  long  been  usual  to  compare  propositions  as  re- 
gards the  quality  of  the  subject  matter  to  which  they 
refer,  and  what  is  technically  called  the  matter  was  dis- 
tinguished into  three  kinds,  necessary,  contingent,  and 
impossible.  Necessary  matter  consists  of  any  subject 
in  which  the  proposition  A  may  be  affirmed ;  impossible 
in  which  E  may  be  affirmed.  Any  subject  or  branch  of 
knowledge  in  which  universal  statements  cannot  usually 
be  made  is  called  contingent  matter,  and  it  implies  the 
truth  of  I  and  0.  Thus  "comets  are  subject  to  gravi- 
tation," though  an  indefinite  or  indesignate  proposition, 
may  be  interpreted  as  A,  because  it  refers  to  a  part  of 
natural  science  where  such  general  laws  obtain.  But 
"men  are  sincere"  would  be  properly  interpreted  as 
particular  or  I,  because  the  matter  is  clearly  contingent. 
The  truth  of  the  following  statements  is  evident : 

In  necessary  matter  A  and  I  are  true  ;  E  and  0  false. 

In  contingent  matter  I  and  0  are  true ;  A  and  E  false. 

In  impossible  matter  E  and  O  are  true  ;  A  and  I  false. 

In  reality,  however,  this  part  of  logical  doctrine  is 
thoroughly  illogical,  because  in  treating  a  proposition 
we  have  no  right,  as  already  explained,  to  assume 
ourselves  acquainted  with  the  science  to  which  it  re- 
fers. Our  duty  is  to  elicit  the  exact  consequences  of 
any  statements  given  to  us.  We  must  learn  in  logic  to 
transform  information  in  every  possible  way,  but  not  to 
add  extraneous  facts. 


98  pROPOsiTioira. 

In  this  section,  on  "Tlie  Opposition  of  Proposi- 
tions," we  have  considered  :— 

1.  The  Ejcplanation  of  the  Four  Propositions, 

2.  Tlie  Distribution  of  Terms, 

3.  The  Table  of  Results. 

4.  The  Itelalions  of  the  Four  Propositions, 
6.  The  Scheme  of  Opposition. 

6.  The  Laws  of  Opjiosition. 

7.  The  Conditions  of  Opposition, 

8.  The  Matter  of  Propositions, 


SECTION    III. 

CONVERSION   AND    IMMEDIATE    INFERENCE. 
1.  The  Nature  of  Inference. 

We  lire  said  to  infer  wheuever  we  draw  one  truth 
from  another  truth,  or  pass  from  one  proposition  to 
another.  As  Sir  W.  Hamilton  says,  Jnfertnceis  '*the 
carrying  out  into  the  last  proposition  what  was  virtually 
contain  ul  in  the  antecedent  judgments."  The  true 
sphere  or  the  science  of  logic  indeed  is  to  teach  the  prin- 
ciples on  which  this  act  of  inference  must  be  performed, 
and  all  the  previous  consideration  of  terms  and  propo- 
sitions is  only  useful  or  pertinent  so  far  as  it  assists  us 
to  understand  the  processes  of  inference.  We  have  to 
consider  in  succession  all  the  modes  in  which  the  same 
information  may  be  moulded  into  different  forms  of 
expression  often  implying  results  of  an  ai)parently 
different  character.  Logifrians  are  not  agreed  exactly 
as  to  what  we  may  include  under  the  name  Inference, 
and  what  we  should  not.     All  would  allow  that  there 


CONVERSION   AND   INFERENCE  87 

is  an  act  of  inference  when  we  see  drops  of  water  on 
the  ground  and  believe  that  it  has  rained.  This  is  a 
somewhat  comphcated  act  of  inference,  which  we  shall 
consider  later  under  the  subject  of  Induction.  Few  or 
none  would  say  that  there  is  an  act  of  inference  in 
passing  from  "  The  Duke  of  Cambridge  is  Commander- 
in-chief,"  to  "The  Commander-in-chief  is  the  Duke  of 
Cambridge."  But  without  paying  much  regard  to  the 
name  of  the  process  I  shall  in  this  section  point  out  all 
the  ways  in  which  we  can  from  a  single  proposition  of 
the  forms  A,  E,  I  or  O,  pass  to  another  proposition. 

*2»  Conversion  of  Propositions. 

We  are  said  to  convert  a  proposition  when  we  trans- 
pose its  subject  and  predicate ;  but  in  order  that  the 
converse  or  converted  proposition  shall  be  inferred  from 
the  convertend,  or  that  which  was  to  be  converted,  we 
must  observe  two  rules  (1)  the  quality  of  the  proposi- 
tion (affirmative  or  negative)  must  be  preserved,  and 
(2)  no  term  must  be  distributed  in  the  Converse  unless 
it  was  distributed  in  the  Convertend. 

(1)  Conversion  by  Limitation. — If  in  "all  metals  are 
elements"  we  were  simply  to  transpose  the  terms,  thus 
— ''all  elements  are  metals,"  we  imply  a  certain  knowl- 
edge about  all  elements,  whereas  it  has  been  clearly 
shown  that  the  predicate  of  A  is  undistributed,  and  that 
the  convertend  does  not  really  give  us  any  information 
concerning  all  elements.  All  that  we  can  infer  is  that 
"some  elements  are  metals;"  this  converse  proposi- 
tion agrees  with  the  rule,  and  the  process  by  which  we 
thus  pass  from  A  to  I  is  called  Conversion  by  Limitation, 
or  Pep  accidens. 


B8  PROPOSITIOlfB. 

('<v)  Simple  Conversion. — When  the  converse  i«»  a 
proposition  of  exactly  the  same  form  as  the  convertend 
the  process  is  called  simple  conversion.  Thus  from 
**some  metals  are  brittle  substances "  I  can  infer  "some 
brittle  substances  are  metals,"  as  all  the  terms  are  here 
undistributed.     Thus  I  is  simply  converted  into  I. 

Again,  from  "no  metals  are  compounds,"  I  can  pass 
directly  to  "  no  compounds  are  metals,"  because  these 
propositions  are  both  in  E,  and  all  the  terms  are  there- 
fore distributed.  Euler's  diagram  (p.  73,  Fig.  3)  clearly 
shows,  that  if  all  the  metals  are  separated  from  all  the 
compounds,  all  the  compounds  are  necessarily  separated 
from  all  the  metals.  The  proposition  E  is  then  simply 
converted  into  E. 

(3)  Conversion  by  Negation. — But  in  attempting  to 
convert  the  proposition  0  we  encounter  a  peculiar 
difficulty,  because  its  subject  is  undistributed  ;  and  yet 
the  subject  should  become  by  conversion  the  predicate 
of  a  negative  proposition,  which  distributes  its  predi- 
cate. Take  for  example  the  proposition,  "some  exist- 
ing things  are  not  material  substances."  By  direct 
conversion  this  would  become  "all  material  substances 
are  not  existing  things;"  which  is  evidently  absurd. 
The  fallacy  arises  from  existing  things  being  distributed 
in  the  converse,  whereas  it  is  particular  in  the  conver- 
tend ;  and  the  rules  of  the  Aristotelian  logic  prevent  us 
from  inserting  the  sign  of  particular  quantity  before 
Ihe  predicate.  The  converse  would  be  equally  untrue 
and  falhicious  were  we  to  make  the  subject  particular, 
as  in  "some  material  substances  are  not  existing 
things."  We  must  conclude,  then,  that  the  proposi- 
tion O  cannot  be  treated  either  by  simple  conversion  o» 


CONVERSION   AND   INFERENCE.  89 

conversion  by  limitation.  It  is  requisite  to  apply  a  new 
process,  which  may  be  called  Conversion  by  Negation, 
and  which  consists  in  first  changing  the  couvertend 
into  an  affirmative  proposition,  and  then  converting  it 
simply.  If  we  attach  the  negation  to  the  predicate 
instead  of  to  the  copula,  the  proposition  becomes  "some 
existing  things  {u*e  irmnaterial  substances,"  and,  con- 
verting simply,  we  have — "some  immaterial  substances 
are  existing  things,"  which  may  truly  be  inferred  from 
the  convertend.  The  proposition  0,  then,  is  only  to 
be  converted  by  this  exceptional  method  of  negation. 

(4)  Contrapositive  Conversion. — Another  process  of 
conversion  can  be  applied  to  the  proposition  A,  and  is 
known  as  conversion  by  contraposition.  From  "all 
metals  are  elements,"  it  necessarily  follows  that  "  all 
not-elements  arc  not  metals."  If  this  be  not  at  the 
first  moment  apparent,  a  little  reflection  will  render  it 
80,  and  from  Fig.* 5  we  see  that  if  all  the  metals  be 

Fig    5 


among  the  elements,  whatever  is  not  element,  or  out- 
side the  circle  of  elements,  must  also  be  outside  the 
circle  of  metals. 

We  may  also  prove  the  truth  of  the  contrapositive  proposi- 
tion in  this  way.    If  what  is  not-element  should  be  metal,  then  it 


00  PROPOSITIONS. 

must  be  an  element  by  the  original  proposition,  or  it  must  be  at  onM 
an  element  and  not  an  element;  which  is  impossible  according 
to  the  Primary  Laws  of  Thought  (Chap.  Ill,  Sect.  I),  since  noth- 
ing  can  both  have  and  not  have  the  same  property.  It  follows 
that  what  is  not-element  must  be  not-metal. 

Mistakes  may  readily  be  committed  in  contrapositive  conver- 
sion, from  a  cause  which  will  be  more  apparent  in  Chapter  VIL 
We  are  very  liable  to  infer  from  a  proposition  of  the  fona  "all 
metals  are  elements,"  that  ail  not-metals  are  not  elements,  which 
is  not  only  a  false  statement  in  itself,  but  is  not  in  the  least 
warranted  by  the  original  proposition.  In  Fig,  5,  it  is  apparent 
that  because  a  thing  lies  outside  the  circle  of  metals,  it  does  not 
necessarily  lie  outside  the  circle  of  elements,  which  is  wider  than 
that  of  metals.  Nevertheless  the  mistake  is  often  made  in  com- 
mon life  ;  and  the  learner  will  do  well  to  remember  that  the  pra 
cess  of  conversion  by  contrajMjsition  consists  only  in  taking  the 
negative  of  the  predicate  of  the  proposition  A,  as  a  new  subject, 
and  affirming  of  it  universally  the  negative  of  the  old  subject. 

Contrapositive  conversion  cannot  be  applied  to  the  particu- 
lar propositions  I  and  0  at  all,  nor  to  the  proposition  E,  in  that 
form ;  but  we  may  change  E  into  A  by  attaching  the  negation  to 
the  predicate,  and  then  the  process  can  be  applied.  Thus  "  no 
men  are  perfect,"  may  be  changed  into  "all  men  are  not  per- 
fect, i.e..  "are  imj)erfect,"  and  then  we  infer  by  contraposition 
"all  not-imperfect  beings  are  not-men."  But  not  imperfect  is 
really  the  same  as  perfect,  so  that  our  new  proposition  is 
really  equivalent  to  "all  {lerfect  beings  are  not  men,"  or  "no 
perfect  beings  are  men,"  (E)  the  simple  converse  of  the  original 
proposition. 

3.  Immediate  Inference. 

There  remain   to  be  described    certain   dednctioni 
which  may  be  drawn  from  a  proposition  without  con« 
verting  its  terms.     They  may  be  called  immediate  in- 
ferences, and  have  been  very  clearly  described  by  Arch 
bishop  Thomson. 


CONVERSION  AND  INFERENOB.  9] 

(1)  Immediate    Inference    by  Privative   Conceptioi! 

consists  in  passing  from  any  affirmative  proposition  to  a 
negative  proposition  implied  in  it,  or  equivalent  to  it, 
or  vice  versa,  in  passing  from  a  negative  proposition  to 
Its  corresponding  affirmative. 

The  following  table  coutaias  a  proposition  of  each  kind  changed 
by  private  conception  into  an  equivalent  proposition 

\  A  all  metals  are  elements. 

^  E   no  raetals  are  compounds. 

j  E  no  men  are  perfect. 

I A  all  men  are  imperfect. 

j  I    some  men  are  trustworthy. 

\  0  some  men  are  not  untrustworthy. 

j  0  some  men  are  not  trustworthy. 

{ I     some  men  are  untrustworthy. 

The  truth  of  any  of  the  above  can  be  clearly  illustrated  by 
diagrams ;  thus  it  will  be  apparent  that  if  the  whole  circle  ol 
metals  lies  inside  the  circle  of  elements,  no  part  can  lie  outside 
of  that  circle  or  among  the  compounds.  Any  of  the  above  prop- 
ositions may  be  converted,  but  the  results  will  generally  be  such 
as  we  have  already  obtained.  Thus  the  simple  converse  of  "  no 
metals  are  compounds  "  is  "  nc  compounds  are  metals,"  or  "  no 
not-elements  are  metals,"  the  contra  positive  of  "  all  metals  are 
elements."  From  the  last  example  we  get  also  by  simple  con- 
version, "  some  untrustworthy  beings  are  men,"  which  is  obvi- 
ously the  converse  by  negation,  as  before  explained.  Applying 
this  kind  of  conversion  to  "some  men  are  not  untrustworthy," 
we  have  "  some  not-untrustworthy  beings  are  men."  Lastly, 
from  "  all  men  are  imperfect "  we  may  obtain  through  conversion 
by  limitation,  "  some  imperfect  beings  are  men." 

(2)  Immediate    Inference    by    Added    Determinants 

consists  in  joining  some  adjective  or  similar  qualifica- 
tion both  to  the  subject  and  predicate  of  a  proposition, 
60  as  to  render  the  meaning  of  each  term  narrower  or 
better  determined.     Provided  that  no  other  alteration 


n  PB0P0SITI0N8. 

18  made,  the  truth  of  the  new  proposition  necessariii 
follows  from  the  truth  of  the  original  in  almost  ail 

cases. 

Protn  "  all  metals  are  elements,"  we  may  tlius  infer  that  "  all 
very  heavy  metals  are  very  heavy  elements."  From  "a  comet  is 
a  material  body  "  we  infer  "  a  visible  comet  is  a  visible  material 
body."  But  if  we  apply  this  kind  of  inference  too  boldly  we 
may  meet  with  fallacious  and  absurd  results.  Thus,  from  "all 
kings  are  men,"  we  might  infer  "all  incompetent  kings  are 
incompetent  men  ;"  but  it  does  not  at  all  follow  tliat  those  who 
are  incompetent  as  kings  would  be  incomjjetent  in  other  posi- 
tions. In  this  case  and  many  others  the  qualifying  adjective  is 
liable  to  bear  different  meanings  in  the  subject  and  predicate, 
but  the  inference  will  only  be  true  of  necessity  when  the  mean- 
ing is  exactly  the  same  in  each  case  With  comparative  terms 
this  kind  of  inference  will  seldom  be  applicable;  thus  from  "a 
cottage  ia  a  building,"  we  cannot  infer  "a  huge  cottage  is  a  huge 
building,"  sib^e  a  cottage  may  be  large  when  compared  with 
other  cottages,  but  not  with  buildings  generally. 

(3)  Immediate  Inference  by  Complex  Conception  is 

closely  similar  to  the  last,  and  consists  in  employing  the 
subject  and  predicate  of  a  proposition  as  parts  of  a 
more  complex  system. 

Prom  "  all  metals  are  elements,"  I  can  pass  to  "  a  miitture  of 
metals  is  a  mixture  of  elements."  From  "a  horse  is  a  quadruped" 
I  infer  "the  skeleton  of  a  horse  is  the  skeleton  of  a  quadruped." 
But  here  again  the  reader  must  beware  of  applying  the  process 
where  the  new  complex  conception  has  a  different  meaning  in 
the  subject  and  predicate.  Thus,  from  "  all  Prc^testants  are 
Christians,"  it  does  not  follow  that  "a  majority  of  Protestants 
are  a  majority  of  Christians,"  nor  that  "  the  most  excellent  of  the 
Protestants  is  the  most  excellent  of  the  Christians." 

The  student  is  recommended  to  render  himself  familiar 
with  all  the  transformations  of  propositions,  or  immediate 


ANALYSIS  OF  SENTENCES.  93 

Interences  described  in  this  lesson ;  and  copious  examples  are 
f umislieil  for  the  purpose.  It  is  a  good  exercise  to  throw  the 
same  proposition  through  a  series  of  changes,  so  that  it  comes 
out  in  its  original  form  at  last,  and  thus  proves  the  truth  of  all 
the  intermediate  changes ;  but  should  conversion  by  limitation 
have  been  used,  the  original  iniversal  proposition  cannot  be 
regained,  but  only  the  particular  proposition  corresponding 
to  it. 
On  Immediate  Inference,  Archbishop  Thomson,  Outline  of  tlte 
Lmc8  of  Thought,  Sections  85-92. 

Ill  this  section,  on  "  Conversion  and  Immediate 
inference,"  we  have  considered : — 

1.  The  Nature  of  Inference, 

2.  Conversion, 

3.  Innnediate  Inference, 


SBCTION   lY. 

THE   LOGICAL  ANALYSIS    OF    SENTENCES 

1.  Relation  of  Logic  to  this  Topic. 

Propositions  as  they  are  usually  to  be  found  in 
written  or  spoken  compositions  seldom  exhibit  the 
simple  form,  the  conjunction  of  a  subject,  copula,  and 
predicate,  which  we  have  seen  to  be  the  proper  logical 
construction.  Not  only  is  the  copula  often  confused 
with  the  predicate,  but  several  propositions  may  be 
combined  into  one  grammatical  sentence.  For  a  full 
account  of  the  analysis  of  sentences  I  shall  refer  to 
several  excellent  little  worlds  devoted  to  the  subject ; 
but  I  will  here  attempt  to  give  a  sketch  of  the  varioua 
ways  in  which  a  sentence  ma-"  be  constructed. 


94  PEOPO'SITTONS. 

2.  The  Grammatical  and  the  Logical  Predicate. 

So  often  is  the  copula  united  to  the  predicate  in 
ordinary  language,  that  the  grammarian  treats  the 
proposition  as  composed  of  only  two  parts,  the  subject 
and  predicate,  or  verb.  Thus  the  proposition,  "  The  sun 
rises,"  apparently  contains  nothing  but  a  subject  *'  the 
Bun,"  and  a  predicate  "  rises ; "  but  the  proposition  is 
really  equivalent  to  "  the  sun  is  rising,"  in  which  the 
copula  is  distinctly  shown.  We  shall,  therefore,  con- 
sider the  verb  or  grammatical  predicate  as  containing 
both  copula  and  logical  predicate.  In  Latin  one  single 
word  may  combine  all  the  three  parts  of  the  proposition, 
as  in  sum,  "I  am ;"  and  the  celebrated  exclamation  of 
Caesar,  Veniy  vidi,  vici,  "I  came,  I  saw,  I  conquered," 
contains  three  distinct  and  complete  propositions  in 
three  words.  These  peculiar  cases  only  arise,  however, 
from  the  parts  of  the  proposition  having  been  blended 
together  and  disguised  in  one  word  ;  and  in  the  Latin 
sum,  the  letter  wi  is  a  relic  of  the  pronoun  me,  which  is 
the  real  subject  of  the  proposition.  If  we  had  a  perfect 
acquamtance  with  the  Giammar  of  any  language  It 
would  probably  not  contradict  the  logical  view  of  a 
sentence,  but  would  perhaps  explain  how  the  several 
parts  of  tlie  complete  proposition  had  become  blended 
and  apparently  lost,  just  as  the  words  tvill  and  not  are 
blended  in  the  colloquial  "I  wont." 

8.  The  Plurality  of  Propositions  In  a  Sentence. 

A  grammatical  sentence  may  contain  any  number  of 
distinct  propositions,  which  admit  of  being  separated 


ANALYSIS  OP  SENTENCES.  95 

but  which  are  combined  together  for  the  sake  of 
brevity.    In  the  sentence, 

"Art  is  long  and  Time  is  fleeting,** 

there  are  two  distinct  subjects,  Art  and  Time,  and  two 
predicates,  "long"  and  "fleeting,"  so  that  we  have 
simply  two  propositions  connected  by  the  conjunction 
2nd.  We  may  have,  however,  several  distinct  subjects 
with  one  and  the  same  predicate ;  as  in 

"  Thirty  days  hath  September, 
April,  June,  and  November.'* 

In  this  well-known  couplet  the  predicate  "  having 
thirty  days "  is  placed  first  for  the  sake  of  emphasis, 
and  there  are  four  subjects,  September,  April,  etc.,  of 
each  of  which  it  is  affirmed.  Hence  these  lines  really 
contain  four  distinct  propositions. 

Again,  there  may  be  one  subject  with  a  plurality  of 
predicates,  so  that  several  different  propositions  are 
asserted  without  the  repetition  of  the  subject  and 
copula.     Thus  the  sentence 

"Nitrogen  is  a  colorless,  tasteless,  inodorous  gas, 
slightly  ligliter  than  air,"  contains  one  subject  only. 
Nitrogen,  but  four  or  five  predicates  ;  it  is  plainly 
equivalent  to  "Nitrogen  is  colorless,"  "Nitrogen  is 
tasteless,"  "Nitrogen  is  a  gas,"  and  so  on. 

Lastly,  we  may  have  several  subjects  and  several 
predicates  all  combined  in  the  same  sentence,  and  with 
only  one  copula,  so  that  each  predicate  is  asserted  of 
each  subject;  and  a  great  number  of  distinct  proposi- 
tions are  condensed  into  one  brief  sentence.  Thus  in 
the  sentence,  "  Iron.  Copper,  r-^ad  and  Zinc  are  abun- 


M  PBOPOsmoifS. 

dant,  cheap  and  useful  metals,"  we  have  evidently  four 
subjects,  and  we  may  be  said  to  have  four  predicates, 
"  abundant,"  "  cheap,"  "  useful,"  and  "  metal."  Ak 
there  is  nothing  to  prevent  our  applying  each  predicate 
to  each  subject  the  sentence  really  contains  16  distinct 
propositions  in  only  11  words;  thus  "Iron  is  abun- 
dant," "Iron  is  cheap,"  "Copper  is  abundant,"  "Cop- 
per is  cheap,"  and  so  on.     In  the  curious  sentence  : 

"  Hearts,  tongues,  figures,  scribes,  bards,  poets,  can- 
not think,  speak,  cast,  write,  sing,  number,  his  love  to 
Antony,"*  Shakspeare  has  united  six  subjects  and  six 
predicates,  or  verbs,  so  that  there  arc,  strictly  speaking, 
six  times  six  or  thirty-six  propositions. 

In  all  the  cases  above  noticed  the  sentence  is  said  to  be  cotTl' 
pound,  and  the  distinct  proi)ositions  combined  together  are  saia 
to  be  co-ordinate  with  each  other,  that  is  of  the  same  order  or 
kind,  because  tliey  do  not  depend  upon  each  other,  or  in  any  way 
affect  each  other's  truth.  The  abundance,  cheapness,  or  utility 
of  iron  need  not  be  stated  in  the  same  sentence  witli  tlie  qualities 
of  copper,  lead  or  zinc  ;  but  as  the  predicates  hap|)en  to  be  the 
same,  considerable  trouble  in  speaking  or  writing  is  saved  by 
putting  as  many  sulyects  as  possible  to  the  same  set  of  predi- 
cates. It  is  truly  said  that  brevity  is  the  soul  of  wit,  and  one  of 
the  great  arts  of  composition  consists  in  condensing  as  many 
statements  as  |>oBsibIe  into  the  fewest  words,  so  long  as  the 
meaning  is  not  confused  thereby. 

4.  Complex   Sentences. 

Propositions  are,  however,  combined  in  a  totally 
different  manner  when  one  proposition  forms  a  part  of 
the  subject  or  predicate  of  the  other.     Thus  in  the 

*  Antony  and  Cleopatra,  Act  III,  Sec.  4. 


1.KALT8I8  OF  SENTENCES.  97 

aentence,  "The  man  who  is  upright  need  not  feai 
accusation,"  there  are  two  verbs,  and  two  propositions, 
but  one  of  these  only  describes  the  subject  of  the  other; 
"who  is  upright"  evidently  restricts  the  application  of 
the  predicate  "  need  not  fear  accusation  "  to  a  part  ot 
the  class  "man."  The  meaning  of  the  whole  sentence 
might  be  expressed  in  the  form 

"The  upright  man  need  not  fear  accusation." 

A.ud  it  is  clearly  seen  that  the  clause  or  apparent  prop- 
osition is  substituted  for  an  adjective.  Such  a  clause 
or  proposition  is  called  subordinate,  because  it  merely 
assists  in  the  formation  of  the  principal  sentence,  and 
has  no  meaning  apart  from  it ;  and  any  sentence  con- 
taining a  subordinate  clause  is  said  to  be  complex. 
Almost  any  part  of  a  sentence  may  thus  be  replaced  by 
a  subordinate  clause.  Thus  in  "  Oxygen  and  Nitrogen 
are  the  gases  which  form  the  largest  part  of  the  at- 
mosphere," there  is  a  subordinate  clause  making  part 
of  the  predicate,  and  the  meaning  might  be  expressed 
nearly  as  well  in  this  way,  "Oxygen  and  Nitrogen  are 
the  gases  forming  the  largest  part  of  the  atmosphere." 


In  the  case  of  a  modal  proposition,  or  one  which  states  the 
manner  in  which  the  predicate  belongs  to  the  subject,  the  mode 
may  be  expressed  either  by  an  adverb,  or  by  a  subordinate 
clause.  "  As  a  man  lives  so  he  dies"  is  such  a  proposition  ;  for 
it  means,  "  a  man  dies  as  he  lives,"  and  "  as  he  lives"  is  equiva- 
lent to  an  adverb;  if  he  lives  well,  he  dies  well;  if  he  lives 
badly,  he  dies  badly.  Adverbs  or  adverbial  cluns^s  may  also 
specify  the  time,  place,  or  any  other  circumstance  concerned  in 
the  truth  of  the  main  proposition. 

Assuming  the  learner  to  be  acquainted  with  the  grammatica.' 

d 


98  PROPOSITIONS. 

terms  ased,  we  may  tlius  state  the  parts  of  which  the  most 
complex  sentence  must  consist. 

The  subject  may  consist  of — 

1.  A  noun  ;  as  m  "  The  Queen  reigns." 

2.  A  pronoun ;  as  in  "  SKe  reigns," 

3.  An  adjective  converted  into  a  noun  ;  as  in  "  WhiUs  are 
titUized." 

4  A  gerund  ;  as  "  Seeing  is  believing." 

5.  An  infinitive ;  as  "  To  see  is  to  believe." 

6.  A  subordinate  clause;  as  "  Who  falls  from  virtue  is  lost. 
The  subject  may  be  qualified  or  restricted  by  combining  with 

Jt  an  attribute  which  may  be  expressed  in  any  of  the  following 
ways: 

1.  An  adjective ;  as  "  Fresh  air  is  wholesome." 

2.  A  participle  ;  as  "  Falling  stars  are  often  seen." 

3.  A  noun  used  as  an  adjective ;  as  "Iron  ships  are  now  much 
employed." 

4.  A  noun  and  preposition;  as  "ships  of  iron  are  now  much 
employed." 

5.  A  possessive  case ;  as  "  Chatham's  son  was  the  great  minister 
Pitt" 

6.  A  noun  m  apposition ;  as  "  The  Metropolis  London  jb  the 
most  ]X)pu1ou8  of  cities." 

7.  A  prerund  or  dative  infinitive  ;  as,  "  The  desire  to  go  abroad 
is  common  in  Englishmen," 

The  predicate  consists  almost  always  of  a  verb,  which  often 
has  some  object  or  qualifying  words  ;  thus  it  may  be — 

1.  A  simple  tense  of  a  complete  verb  ;  as  "  The  sun  rises." 

2.  A  compound  tense  ;  as  "  The  sun  has  risen. ' 

3.  An  incomplete  verb  and  complement ;  as  "  The  sea  appears 
rough." 

4.  The  verb  "to  be"  and  an  adjective;  as  "Time  is  fleeting." 

5.  A  verb  with  an  object;  as  "  Warmth  nwltn  ice." 

i.  A  verb  with  an  adverbial ;  as  "  The  snow  falls  thieMy." 

The  object  of  a  verb  is  usually  a  noun  or  pronoun,  but  any 
other  of  the  six  kinds  of  expressions  which  may  serve  as  a  sub 
{ect  laay  sJso  serve  as  an  object 


ANALYSIS   OF   SENTENCES.  99 

The  adverbial  qualifying  a  verb  and  expressing  the  manner, 
time,  place,  or  other  circumstaDce  affecting  the  proposition  may 
be— 

1.  An  adverb  ;  as  "  The  days  pass  slowly." 

2.  A  noun  and  preposition  ;  as  "  The  resolution  was  passed  by 
a  large  majority." 

3.  An  absolute  phrase ;  as  "  The  snow  melts,  the  sun  homng 
risen." 

4  A  dative  infinitive  ;  as  "  She  stoops  to  conquer." 
5.  Any  phrase  equivalent  to  an  adverb;  as  "The  dividends 
are  paid  ticice  a  year." 

5,. Modes  of  Exhibiting  Construction. 

Various  modes  of  exhibiting  the  construction  of  sen- 
tences by  symbols  and  names  for  the  several  parts  have 
been  invented  ;  but  I  believe  that  by  far  the  simplest 
and  most  efficient  mode  is  to  exhibit  the  construction 
in  the  form  of  a  diagram.  Any  two  or  more  parts  of  a 
sentence  which  are  co-ordinate  with  each  other,  or  bear 
the  same  relation  to  any  other  part,  are  written  along- 
side each  other,  and  coupled  together  by  a  bracket; 
thus  the  diagram, — 


Iron 
Copper 
Lead 
Zinc 


>   are   < 


abundant, 
cheap, 
useful 
metals, 

clearly  shows  that  there  are  four  co-ordinate  subjects, 
and  four  co-ordinate  pi-edicates  in  the  example  pre- 
viously taken. 

Whenever  one  part  of  a  sentence  is  subordinate  to 
another  part  it  may  be  connected  with  it  by  a  line 
drawn  in  any  convenient  direction.  Thus  the  analysis 
of  the  following  sentence  is  readily  sliown  by  the  dia- 
gram below  it  : — 


100  PEOP08ITION8. 

"  No  one  who  is  a  lover  of  money,  a  lover  of  pleasure, 
and  a  lover  of  glory,  is  likewise  a  lover  of  mankind ; 
but  only  he  who  is  a  lover  of  virtue." 

i  a  lover  of  money, 
who  is  -<  a  lover  of  pleasure, 
I        (  a  lover  of  glory. 

heVnly 'is  [  ^  ^^^^^  ^^  mankind, 

who  is  a  lover  of  virtue. 
We  see  that  the  sentence  is  both  compound  and  com- 
plex, that  is  to  say  it  contains  two  principal  co-ordinate 
propositions  with  a  common  predicate,  "a  lover  of 
mankind."  The  first  proposition  is  negative  and  its 
subject  is  described  by  three  subordinate  clauses,  while 
the  second  proposition  is  affirmative  and  has  one  sub- 
ordinate clause. 

The  learner  may  be  helped  by  the  analysis  of  a  few  sentences, 
of  which  the  first  consists  of  some  remarkably  complex  lines 
from  a  poem  of  Burbidge : 

"  He  who  metes,  as  we  should  mete, 
Could  we  His  insight  use,  shall  most  approve, 
Not  that  whicli  fills  most  space  in  earthly  eyes, 
But  what — though  Time  scarce  note  it  as  he  flies — 
Fills,  like  this  little  daisy  at  my  feet, 
Its  function  best  of  diligence  in  love." 

which  fills  most  space  in  earthlv  eyes 

I 1 

He  shall  most  approve  j^;;^^  j,^^  ^^ 

who  metes  its  function  of      like  this  little 

'  i      ,,       ,         diligence  in  dai^y  at  my 

as  we  should  mete       j^^^  f^.^^; 

could  we  His  insight  use.  though  Tl^e  scarcl'note  it 

as  he  fiiea 


ANALYSIS   OF   SENTENCES.  101 

"  Most  sweet  it  is  with  unuplifted  eyes 

To  pace  the  ground,  if  path  there  be  or  none, 

While  a  fair  region  round  the  traveler  lies 

Which  he  forbears  again  to  look  upon  ; 

Pleased  rather  with  some  soft  ideal  scene, 

The  work  of  fancy,  or  some  happy  tone 

Of  meditation  slipping  in  between, 

The  beauty  c  milng,  and  the  beauty  gone." 

Wordsworth, 

It  is  most  sweet 

I 
To  pace  the  ground 

with  unuplifted  if  path  while  a  fair  region 

^'yes  ^jjgj.g  i  be  round  the       I 

(  or  none  traveler  lies   | 

wnich  (region)  he  (the  traveler)  forbears  to  look  upon 

I  (  some  soft  ideal  scene 

pleased         J  i 1 

rather  with      )  the  work  of  fancy 

(  or  some  happy  tone  of  meditation 

slipping  in  between  the  beauty  coming 
and  the  beauty  gone. 

In  the  above  sentence  there  is  evidently  one  subject,  "  to  pace 
the  ground,"  which  by  means  of  the  pronoun  it.  is  connected  with 
the  predicate  mostsioeet.  The  main  part  of  the  sentence,  however, 
consists  of  three  adverbials,  expressing  the  manner  and  surround- 
ing circumstances,  and  the  third  adverbial  is  developed  in  a  very 
complicated  manner.  The  sentence  is  not  compound,  but  is 
complex  on  account  of  four  subordinate  propositions. 

In  the  following  sentence  th.'re  is  strictly  but  one  principal 
proposition,  "We  find."  but  this  is  only  a  mode  of  introducing 
the  true  purjxtrt  of  the  senttMice,  "  the  two  classes  of  intellectual 
operations  have  much  that  is  different,  much  that  is  common." 

"  When  the  notions  with  which  men  are  conversant  in  the 
common  course  of  life,  which  give  meaning  to  their  familiar 
language  and  which  give  employment  to  tlieir  hourly  thoughts, 
are  compared  with  the  ideas  on  which  exact  science  is  founded, 


103 


PROPOSITIONS. 


we  find,   that  the  two  classes  of  intellectual  operations  have 

much  that  is  different,  much  that  is  common." 

we  find — that  the  two  classes  (*  f ) 

I  of  intellectual     <  much  that  is  different 

I  operations  have  ( much  that  is  common 

When  the  notions  *  are  compared I 


which  give 
meaning 
to  their 
familiar 
language 


with  the  ideas  f 


which  give 
employ-  | 

ment  to  on  which 

their  hourly  exact  science  is 
thoughts  founded. 


with  which 
men  are 
conversant 
in  the 
common 
course 
of  life 

Here  the  two  classes  form  a  collective  term,  and  have  two  co- 
ordinate predicates  rendering  the  sentence  so  far  a  compound  one. 
The  greater  part  of  the  sentence,  however,  consists  of  a  compli- 
cated subordinate  sentence  of  the  nature  of  an  adverbial,  express- 
ing the  time  or  occasion  when  this  is  found  to  be  the  case. 
As  a  last  example  we  take  the  sentence  given  below : — 
"The  law  of  gravitation,  the  most  universal  truth  at  which 
human  reason  has  yet  arrived,  expresses  not  merely  the  general 
fact  of  the  mutual  attraction  of  all  matter ;  not  merely  the  vague 
statement  that  its  influence  decreases  as  the  distance  increases, 
but  the  exact  numerical  rate  at  which  that  decrease  takes  place  ; 
so  that  when  its  amount  is  known  at  any  one  distance  it  may  be 
exactly  calculated  for  any  other." 

at  which  human  reason  has  yet  arrived 

the  most  universal  truth 
I 
The  law  of  gravitation  expresses 


not  merely  the 
general  fact 

of  the  mutual 

attraction  of  all 

matter 


not  merely  the 
vague  statement 

that  its  influence 
decreases 

I 

as  the  distance 

increases 


but  the  exact 
numerical  rate 

I 

at  which  that 

decrease  takeo 

place 


so  that  its  amount  may  be  calculated  for  any  other  distance 

I 
when  it  is  known  at  any  one  distance. 


ANALYSIS   OF  SENTENCES.  103 

W.  S.  Dalgleish's  Qrammatical  Anodym,  or  J.   D.  Morell's 

Analysis  of  Sentences. 
Alexander  Bain's  English  Composition  and  Rhetoric,  pp.  91-117, 

treats  of  construction  of  sentences. 

In  thi.s  section,  on   "The  Logical  Analysis    of 
Sentences,"  we  have  considered:— 

1.  The  Relation  of  Logic  to  this  Topic. 

2.  The  Grumniatical  and  the  Logical  Predicate. 

3.  The  Plurality  of  Propositions  in  a  Sentence, 

4.  Complex  Sentences. 

6.  Modes  of  Exhibiting  Construction. 


CHAPTER    HI. 
SYLLOGISMS. 

The  subject  of  Syllogisms  will  be  considered 
under  the  following  divisions  :  (1)  The  Laws  of 
Thomjht;  (2)  The  Mules  of  the  Syllogism; 
(3)  The  Moods  and  Fiffures  of  the  Syllo- 
yism;    (4)  The  Rednctioti    of  Syllogisms; 

(5)  Irregnlar  atid  Coinj^oinid  Syllogisms; 

(6)  Condifiontii  Syllogisms, 


SECTION    I. 

THE    LAWS   OF  THOUGHT. 

1.  The  Statement  of  the  Primary  Laws  of 
Thoiig-ht. 

Before  proceeding  to  examine  the  structure  of  the 
Syllogism  and  the  rules  that  govern  it,  it  is  desirable 
that  the  learner  should  give  a  careful  attention  to  the 
very  simple  laws  of  thought  on  which  all  reasoning 
must  ultimately  depend.  These  laws  describe  the  very 
simplest  truths,  in  which  all  people  must  agree,  and 
which  at  the  same  time  apply  to  all  notions  which  we 
can  conceive.  It  is  impossible  to  think  correctly  and 
avoid  evident  self-contradiction  unless  we  observe  what 
are  called  tlie  Three  Primapy  Laws  of  Thought,  which 
may  be  stated  as  follows  : 


LAWS   OF  THOUGHT.  106 

1.  The  Law  of  Identity.     Whatever  is,  is. 

2.  The  Law  of  Contradiction.     Nothing  can  both  be 

and  not  be. 

3.  Tlie  Law  of  Excluded  Middle.     Everything  must 

either  be  or  not  be. 

Though  these  laws  when  thus  stated  may  seem  absurdly 
obvious,  and  were  ridiculed  by  Locke  and  others  on  that  account, 
students  are  seldom  able  to  see  at  first  their  full  meaning  and 
importance.  All  arguments  may  be  explained  wlu-n  these  self- 
evident  laws  are  granted  ;  and  it  is  not  too  much  to  say  that  the 
whole  of  logic  will  be  plain  to  those  who  will  constantly  use 
these  laws  as  the  key, 

2.  Explanation  of  the  Laws. 

(1.)  Law  of  Identity, — The  first  of  the  laws  may  be 
regarded  as  the  best  definition  we  can  give  of  identity 
or  sameness.  Could  any  one  be  ignorant  of  the  mean- 
ing of  the  word  Identity,  it  would  be  sufficient  to  in- 
form him  that  everything  is  identical  with  itself, 

(2.)  Law  of  Contradiction. — The  second  law,  how- 
ever, is  one  which  requires  more  consideration.  Its 
meaning  is  that  nothing  can  have  at  the  same  time  and 
at  the  same  place  contradictory  and  inconsistent  quali- 
ties. A  piece  of  paper  may  be  blackened  in  one  part. 
while  it  is  white  in  other  parts  ;  or  it  may  be  white  at 
one  time,  and  afterwards  become  black:  but  we  cannot 
conceive  that  it  should  be  both  white  and  l>lack  at  the 
same  place  and  time.  A  door  after  being  open  may  he 
shut,  but  it  cannot  at  once  be  shut  and  open.  Water 
may  feel  warm  to  one  hand  and  cold  to  another  hand, 
but  it  cannot  be  both  warm  and  cold  to  the  same 
hand.     No  quality  can  both  be  present  and  absent  at 


106  SYLLOGISMS. 

the  same  time ;  and  this  seems  to  be  the  most  simple 
and  general  truth  which  we  can  assert  of  all  things.  It 
is  the  very  nature  of  existence  that  a  thing  cannot  be 
otherwise  than  it  is  ;  and  it  may  be  safely  said  that  all 
fallacy  and  error  arise  from  unwittingly  reasoning  in  a 
way  inconsistent  with  this  law.  All  statements  or  in- 
ferences which  imply  a  combination  of  contradictory 
qualities  must  be  taken  as  impossible  and  false,  and  the 
breaking  of  this  law  is  the  mark  of  their  being  false. 
It  can  easily  be  shown  that  if  Iron  be  a  metal,  and 
every  metal  an  element,  Iron  must  be  an  element  or  it 
can  be  nothing  at  all,  since  it  would  combine  qualities 
wliich  are  inconsistent. 

(3)  The  Law  of  Excluded  Middle  is  much  less  self- 
evident  than  either  of  the  two  preceding  ones,  and  the 
learner  will  not  perhaps  see  at  the  first  moment  that  it 
is  equally  important  and  necessary  with  them.  Its 
meaning  may  be  best  explained  by  saying  that  it  is  im- 
possible to  mention  any  thimj  and  any  qnality  or  cir- 
cumstance, without  allowing  that  the  quality  or  circum- 
stance either  belongs  to  the  thing  or  does  not  belong. 
The  name  of  the  law  expresses  the  fact  that  there  is  no 
third  or  middle  course  ;  the  answer  must  be  Yes  or  No. 
Let  the  thing  be  rock  and  the  quality  hard ;  then  rock 
must  be  either  hard  or  not-hard.  Gold  must  be  either 
white  or  not  white;  a  line  must  be  either  straight  or 
not  straight ;  an  action  must  be  either  virtuous  or  not 
virtuous.  Indeed,  when  we  know  nothing  of  the  terms 
used  we  may  nevertheless  make  assertions  concerning 
them  in  accordance  with  this  law.  The  learner  may 
not  know,  and  in  fact  chemists  may  not  really  know 
with  certainty,  whether  vanadium  is  a  metal  or  not  a 


LAWS   OF  THOUGHT.  107 

metal,  but  any  one  knows  that  it  must  be  one  or  the 
other.  Some  learners  may  not  know  what  a  cycloid  is, 
or  what  an  isochronous  curve  is  ;  but  they  must  know 
that  a  cycloid  is  either  an  isochronous  curve  or  it  is 
not  an  isochronous  curve. 

This  law  of  excluded  middle  is  not  so  evident  but  that  plausible 
objections  may  be  suggested  to  it.  Rock,  it  may  be  urged,  is 
not  always  either  liard  or  soft,  for  it  may  be  half-way  between, 
a  little  hard  and  a  little  soft  at  the  same  time.  This  objection 
points  to  a  distinction  which  is  of  great  logical  importance,  and 
when  neglected  often  leads  to  fallacy.  The  law  of  excluded 
middle  affirmed  nothing  about  hard  and  soft,  but  only  referred  to 
hard  &nd  not-hai'd ;  if  the  reader  chooses  to  substitute  soft  for 
not-hard  he  falls  into  a  serious  confusion  between  opposite  terms 
and  contradictory  terms.  It  is  quite  possible  that  a  thing  may 
be  neither  hard  nor  soft,  being  half  way  between ;  but  in  that 
case  it  cannot  be  fairly  called  hard,  so  that  the  law  holds  true. 
Similarly  water  must  be  either  warm  or  not-warm,  but  it  does 
not  follow  that  it  must  be  warm  or  cold.  The  alternative  not- 
warm  evidently  includes  all  cases  in  which  it  is  cold  besides 
cases  where  it  is  of  a  medium  temperature,  so  that  we  should  call 
it  neither  warm  nor  cold.  We  must  thus  carefully  distinguish 
questions  of  degree  or  quantity  from  those  of  simple  logical 
fact.  In  cases  where  a  thing  or  quality  may  exist  to  a  greater  or 
less  extent  there  are  many  alternatives.  Warm  water,  for  in- 
stance, may  have  any  temperature  from  70"  perhaps  up  to  120'. 
Exactly  the  same  question  occurs  in  cases  of  geometrical  reason- 
ing ;  for  Euclid  in  his  Elements  frequently  argues  from  the  self- 
evident  truth  that  any  line  must  be  either  greater  than,  equal  to, 
or  less  than  any  other  line.  While  there  are  only  two  alternatives 
to  choose  from  in  logic  there  are  three  in  Mathematics  ;  thus  one 
line,  compared  with  another,  may  be — 

! greater .  .  .greater  )  ^ 

not  greater. .  j  ; ; ;  -j^^^^'      \  Mathematics. 

Another  and  even  more  plausible  objection  may  be  raised  to 


108  SYLLOGISMS. 

the  third  law  of  thought  in  this  way.  Virtue  being  the  thing 
proi)()S('d,  and  triangular  the  quality,  the  Law  ot  Excludes 
Middle  enablea  us  at  once  to  assert  that  virtue  is  either  triangulai 
or  not  triangular.  At  first  sight  it  might  seem  false  and  absurd 
to  say  that  an  immaterial  notion  such  as  virtue  should  be  either 
triangular  or  not,  because  it  has  nothing  in  common  witii  those 
material  substances  occupying  space  to  wliich  the  notion  of  figure 
belongs.  But  the  absurdity  would  arise,  not  from  any  falseness 
in  the  law,  but  from  misinterpretation  of  the  expression  not- 
triangrdar.  If  in  saying  that  a  thing  is  "not  triangular"  we  are 
taken  to  imply  that  it  has  some  figure  though  not  a  triangular 
figure,  then  of  course  the  expression  cannot  be  applied  to  virtue 
or  anything  immaterial.  In  strict  logic,  however,  no  such  im- 
plied meaning  is  to  be  allowed,  and  not-triangular  will  include 
both  things  which  have  figure  other  than  triangular,  as  well  aa 
things  wiiich  have  not  the  properties  of  figure  at  all  ;  and  it  ia 
in  the  latter  meaning  that  it  is  applicable  to  an  immaterial  thing 

3.  The  Canons  of  Syllogism. 

These  three  laws  then  being  universally  and  neces- 
sarily true  to  whatever  things  they  are  applied,  become 
the  foundation  of  reasoning.  All  acts  of  reasoning 
proceed  from  certain  judgments,  and  the  act  of  judg- 
ment consists  in  comparing  two  things  or  ideas  together 
and  discovering  whether  they  agree  or  differ,  that  is  to 
say  whether  they  are  identical  in  any  qualities.  The 
laws  of  thought  inform  us  of  the  very  nature  of  this 
identity  with  which  all  thought  is  concerned.  But  in 
the  operation  of  discourse  or  reasoning  we  need  certain 
additional  laws,  or  axioms,  or  self-evident  truths,  which 
may  be  thus  stated  : 

1.  Tivo  terms  agreeing  with  one  and  the  same  third 
term  agree  with  each  other. 

9.   Two  terms  of  which  one  agrees  and  the  other  doet 


LAWS  OF  THOUGHT.  100 

not  agree  with  one  and  the  same  third  term,  do  not  agree 
with  each  other. 

3.  Two  terms  both  disagreeing  loith  one  and  the  sanu 
third  term  may  or  may  not  agree  ivith  each  other. 

These  self-evident  truths  are  commonly  called  the 
Canons  or  Fundamental  Principles  of  Syllogism. 

They  are  true,  whatever  may  be  the  kind  of  agreement  in 
question.  The  example  we  formerly  used  (p.  3)  of  the  aj^ree- 
ment  of  the  terms  "  Most  useful  metai "  and  "  cheapest  metal  " 
with  the  third  common  term  "  Iron,"  was  but  an  instance  of  the 
first  Canon,  and  the  agreement  consisted  in  complete  identity. 
In  the  case  of  the  "  Earth,"  the  "  Planets,"  and  "  Bodies  revolv- 
ing in  elliptic  orbits,"  the  agreement  was  less  complete,  because 
the  Earth  is  only  one  of  many  Planets,  and  the  Planets  only  a 
email  portion  of  all  the  heavenly  bodies,  such  as  Satellitea 
Comets,  Meteors,  and  Double-Stars  which  revolve  in  such  orbits* 

The  second  of  the  Canons  applies  to  cases  where  there  is  di» 
•greement  or  difference,  as  in  the  following  example : 

Venus  is  a  planet. 

Planets  are  not  self-luminous. 

Therefore  Venus  is  not  selflumlnoaa 

The  first  of  these  propositions  states  a  certain  agreement  to 
•xist  between  Venus  and  planet,  just  as  in  the  previous  case  of 
the  Earth,  but  the  second  proposition  states  a  disafjreement  l)e 
tween  Planet  and  self  luminous  bodies:  hence  we  infer  a  dis- 
agreement between  Venus  and  self  luminous  body.  But  the 
learner  will  carefully  observe  that /rom  tiM  disagreements  ite  car, 
never  infer  anything.  If  the  following  were  put  forth  as  au 
argument  it  would  be  evidently  absurd  : — 

Sirtus  is  not  a  planet. 
Planets  are  not  self-luminous. 
Therefore  Sirius  is  not  self-luminou* 

%)th  the  premises  or  propositions  given  are  true,  and  yet  thi 


110  SYLLOGISMS. 

conclosion  is  false,  for  all  the  fixed  stars  are  Belf-laminoHriti  %t 
shine  by  their  own  light.     This  illustrates  the  third  Caaon. 

4.  The  Axioms  of  Mathematics. 

Self-evident  rules,  of  an  exactly  similar  nature  to 
these  three  Canons,  are  the  basis  of  all  mathematical 
reasoning,  and  are  usually  called  axioms.  Euclid's  first 
axiom  is  that  "Things  which  are  equal  to  the  samo 
thing  are  equal  to  one  another;"  and  whether  we 
apply  it  to  the  length  of  lines,  the  magnitude  of  angles, 
areas,  solids,  numbers,  degrees,  or  anything  else  which 
admits  of  being  equal  or  unequal,  it  holds  true.  Thu? 
if  the  lines  A  and  B  are  each  equal  to  C  it  is  evider:1 
that  each  is  equal  to  the  other. 

A 

B — 


B. 


Euclid  does  not  give  axioms  correspondmg  to  the 
second  and  third  Canons,  but  they  are  really  used  in 
Geometry.  Thus  if  A  is  equal  to  B,  but  D  is  not 
equal  to  B,  it  follows  that  A  is  not  equal  to  D,  or 
things  of  which  one  is  equal,  but  the  other  unequal  to 
the  same  third  thing,  are  unequal  to  each  other.  Lastly, 
A  and  E  are  two  lines  both  unequal  to  D  and  un- 
equal to  each  other,  whereas  A  and  B  are  two  lines  both 
unequal  to  D  but  equal  to  each  other;  thus  we  plainly 
see  that  *'  two  things  both  unequal  to  the  same  thing 
may  or  may  not  be  equal  to  each  other." 

Prom  what  prect-xles  it  will  be  apparent  that  all  reasoning  rt« 


LAWS  OF  THOUGHT.  Ill 

quires  thsMhere  should  be  one  agreement  at  least;  if  thero 
be  iwo  agi-eements  we  may  reason  to  a  third  agreement ;  if  tber« 
be  one  agrtsement  and  one  difference  we  may  reason  to  a  second 
diflference ;  but  if  there  be  two  differences  only  we  cannot  reason 
to  an/  conclusion  whatever.  These  self-evident  principles  will 
in  the  next  Lesson  serve  to  explain  some  of  the  rules  of  the 
Syllogism. 

5.  Aristotle's  Dicta. 

Logicians,  however,  have  not  confined  themselvss  to 
the  use  of  these  Canons,  but  have  often  put  the  same 
truth  into  a  different  form  in  axioms  known  as  the 
Dicta  de  omni  et  nullo  of  Aristotle.  This  celebrated 
Latin  phrase  means  "Statements  conceraing  all  and 
none,"  and  the  axiom,  or  rather  pair  of  axioms,  is 
usually  given  in  the  following  words : 

Whatever  is  predicated  of  a  term  distributed,  lohether 
affirmatively  or  negatively,  may  he  predicated  in  like 
7na?iner  of  everything  contained  under  it. 
Or  more  briefly: 

What  pertains  to  the  higher  class  pertains  also  to  the 
lower. 

This  merely  means,  in  untechnical  language,  that  what  may 
be  said  of  all  tlie  things  of  any  sort  or  kind  may  be  said  of  any 
one  or  any  part  of  those  things ;  and,  secondly,  what  may  be 
denied  of  all  the  things  in  a  class  may  be  denied  of  any  one  or 
any  part  of  them.  Whatever  may  be  said  of  "  All  planets  "  may 
be  said  of  Venus,  the  Earth,  Ju^siter,  or  any  other  planet ;  and, 
as  they  may  all  be  said  to  revolve  in  elliptic  orbits,  it  follows 
that  this  may  be  asserted  of  Venus,  the  Earth,  Jupiter,  or  any 
other  planet.  Similarly,  according  to  the  negative  part  of  the 
Dicta,  we  may  deny  that  the  planets  are  self  luminous,  and  know- 
ing that  Jupiter  is  a  planet  may  deny  that  Jupiter  is  self-lumi- 
nous. A  little  reflection  would  show  that  the  affirmative  Dictum 
is  really  the  first  of  the  Canons  in  a  less  complete  and  general 
form,   and   that  the   negative   Dictum   is   similarly  the  second 


1 12  SYLLOGISMS. 

Canon.  These  Dicta,  in  fact,  only  apply  to  sucli  cases  of  agree 
inent  between  terms  as  consist  in  one  being  the  name  of  a  smaller 
class,  and  another  of  the  larger  class  containing  it.  Logicians 
have  for  the  most  part  strangely  overlooked  the  important  cases 
in  which  one  term  agrees  with  another  to  the  extent  of  being 
identical  with  it ;  but  this  is  a  subject  which  we  cannot  fitly  dis- 
cuss here  at  any  length,  it  is  treated  in  my  little  work  called  The 
Substitution  of  Similars* 

Some  logicians  have  held  that  in  addition  to  the  three  laws 
which  are  called  the  Primary  Laws  of  Tliought,  there  is  a  fourth 
called  "  The  Principle  or  Law  of  Sufflcient  Reason."  It  was 
stated  by  Leibnitz  in  the  following  words : 

"  Nothing  happens  without  a  reason  why  it  shoiUd  be  so  rather 
than  otherwise.  For  instance,  if  there  be  a  pair  of  scales  in  every 
respect  exactly  alike  on  each  side  and  with  exactly  equal  weights 
in  each  scale,  it  must  remain  motionless  and  in  equilibrium,  be- 
cause there  is  no  reason  why  one  side  should  go  down  more  than 
the  other.  It  is  certainly  a  fundamental  assumption  in  mechani 
cal  science  that  if  a  body  is  acted  upon  by  two  perfectly  equal 
forces  in  different  directions  it  will  move  equally  between  them, 
because  there  is  no  reason  why  it  should  move  more  to  one  side 
than  the  other.  Mr.  Mansel,  Sir  W.  Hamilton  and  othera  consider, 
however,  that  this  law  has  no  place  in  logic,  even  if  it  can  be 
held  self-evident  at  all ;  and  the  question  which  appears  open  to 
doubt  need  not  be  discussed  here. 

I  have  so  freely  used  the  word  axiom  in  this  lesson  that  it  is 
desirable  to  clear  up  its  meaning  as  far  as  |X)8sible.  Philosophers 
do  not  perfectly  agree  about  its  derivation  or  exact  meaning,  but 
it  certainly  comes  from  the  verb  u^iou,  which  is  rendered,  to  think 
wrrthy.  It  generally  denotos  a  self  evident  truth  of  so  simple  a 
character  that  it  must  be  assumed  to  be  true,  and,  a.s  it  cannot 
be  proved  by  any  simpler  proposition,  must  itself  be  taken  as  the 
basis  of  reasoning.  In  mathematics  it  is  clearly  used  in  thi« 
■ense. 

See  Hamilton's  Lectures  on  Logic,  Lectures  5  and  6. 
•  Macmillan  St  Co..  1869. 


LAWS  OF  THOUGHT.  113 

In  this  Section,  on  "Tlie  Laws  of  Tlioiight,'*  we 
have  considered:— 

1.  Statement  of  the  PHinary  Laws  of  Thought, 

2.  The  Explanation  of  the  Laws. 

3.  The  Canons  of  the  Syllogism. 

4.  The  Axioms  of  Mathematics. 

5.  Aristotle's  I>icta, 


SECTIOK    n, 

THE   RULES   OF  THE    SYLLOGISM. 

1.  Tlie  Definition  of  "  Syllogism." 

Syllogism  is  the  common  name  for  mediate  Inference, 
or  inference  by  a  medium  or  middle  term,  and  is  to  be 

distinguislied  from  the  process  of  immediate  inference, 
or  inference  which  is  performed  without  the  use  of  any 
third  or  middle  term. 

The  name  Syllogism  means  the  joining  together  in 
thought  of  two  propositions,  and  is  derived  from  the 
Greek  words  ovv,  with,  and  Xoyog,  thought  or  reason. 
It  is  thus  exactly  the  equivalent  of  the  word  Computa- 
tion, which  means  thinking  together,  (Latin  con,  to- 
gether, piito,  to  think),  or  reckoning.  In  a  syllogism 
we  so  unite  in  thought  two  premises,  or  propositions 
put  forward,  that  we  are  enabled  to  draw  from  them  or 
infer,  by  means  of  the  middle  term  they  contain,  a 
third  proposition  called  the  conclusion.  SyUogism  may 
thus  be  defined  as  the  act  of  thought  by  which  from 
two  given  propositions  we  proceed  to  a  third  proposi- 


114  SYLLOGISMS. 

tion,  the  truth  of  which  'necessarily  follows  from 
the  truth  of  these  given  propositions.  When  the 
argument  is  fully  expressed  in  language  it  is  usual  to 
call  it  concretely  a  syllogism. 

2.  The  Meaning  of  "Middle  Term." 

We  are  in  the  habit  of  employing  a  middle  term,  oi 
medium,  whenever  we  are  prevented  from  comparing 
two  things  together  directly,  but  can  compare  each 
of  them  with  a  certain  third  thing.  We  cannot  com- 
pare the  sizes  of  two  halls  by  placing  one  in  the  other, 
but  we  can  measure  each  by  a  foot-rule  or  other  suit- 
able measure,  which  forms  a  common  measure,  and 
enables  us  to  ascertain  with  any  necessary  degree  of 
accuracy  their  relative  dimensions.  If  we  have  two 
quantities  of  cotton  goods  and  want  to  compare  them,  it 
is  not  necessary  to  bring  the  whole  of  one  portion  to 
the  other,  but  a  sample  is  cut  off,  which  represents 
exactly  the  quality  of  one  portion,  and,  according  as 
this  sample  does  or  does  not  agi'ee  with  the  other  por- 
tion, so  must  the  two  portions  of  goods  agree  or  differ. 

3.  The  Use  of  Middle  Term  in  Syllogism. 

The  use  of  a  middle  term  in  syllogism  is  closely 
parallel  to  what  it  is  in  the  above  instances,  but  not 
exactly  the  same.  Suppose,  as  an  example,  that  we 
wish  to  ascertain  whether  or  not  "  Whales  are  vivipa- 
rous," and  that  we  had  not  an  opportunity  of  observ- 
ing the  fact  directly ;  we  could  yet  show  it  to  be  so  it 
we  knew  that  "  whales  are  mammalian  animals,"  and 
that  "all  mammalian  animals  are  viviparous."  It 
would  follow  that  "  whales  are  viviparous ; "  and  so 


LAWS  OP  THOUGHT.  115 

far  as  the  inference  is  concerned  it  does  not  mattei 
what  is  the  meaning  we  attribute  to  the  words  vivip 
arous  and  mammalian.  In  this  case  ' '  mammaliai 
animal "  is  the  middle  term. 

4.  Statement  of  the  Rules  of  the  Syllogism, 

The  special  rules  of  the  syllogism  are  founded  upou 
the  Laws  of  Thought  and  the  Canons  considered  in  the 
previous  section.  They  serve  to  inform  us  exactly 
under  what  circumstances  one  proposition  can  be  in- 
ferred from  two  other  propositions,  and  are  eight  in 
number,  as  follows : 

1.  Every  syllogism  has  three  and  only  three  terms. 
These  terms  are  called  the  major  term,  the  minor 

term,  and  the  middle  term. 

2.  Every  syllogism  contains  three,  and  only  three 
propositions. 

These  propositions  are  called  the  major  premise,  the 
minor  premise,  and  the  conclusion. 

3.  The  middle  term  must  be  distrihuted  once  at  least, 
and  must  not  be  ambiguous. 

4.  No  term  must  be  distributed  in  the  conclusion 
which  loas  not  distributed  in  one  of  the  premises. 

5.  From  negative  premises  nothing  can  be  inferred. 

6.  If  one  premise  be  negative,  the  conclusion  must  be 
negative  ;  and  vice  versa,  to  prove  a  negative  conclusion 
one  of  the  premises  must  be  negative. 

From  the  above  rules  may  be  deduced  two  subordi- 
nate rules,  which  it  will  nevertheless  be  convenient  to 
state  at  once. 

7.  From  two  'particular  premises  no  conclusion  can  bi 
drawn. 


116  STLLOGISHS. 

8.  If  one  premise  he  particular y  the  conclusion  must 
ie  particular. 

All  these  rules  are  of  such  extreme  imporiauce  that  it  will  be 
desirable  for  the  student  not  only  to  acquire  a  perfect  comprehen- 
sion of  their  meaning  and  truth,  but  to  commit  them  to  memory. 
During  the  remainder  of  this  section  we  shall  consider  theii 
meaning  and  force, 

5.  Explanation  of  the  Rules. 

The  following  is  a  detailed  explanation  of  each  of  the 
rules  already  stated : 

(1)  The  First  Rule. — As  the  syllogism  consists  in 
compariftg  two  terms  by  means  of  a  middle  term,  there 
cannot  of  course  be  less  than  three  terms,  nor  can  there 
be  more ;  for  if  there  were  four  terms,  say  A,  B,  C,  D, 
and  we  compared  A  with  B  and  G  with  D,  we  should 
either  have  no  common  medium  at  all  between  A  and 
Df  or  we  should  require  a  second  syllogism,  so  as  first 
to  compare  A  and  C  with  B,  and  then  A  and  D  with  C. 

The  middle  term  may  always  be  known  by  the  fact 
that  it  does  not  occur  in  the  conclusion.  The  major 
term  is  always  the  predicate  of  the  conclusion,  and  the 
minor  term  the  subject.  These  terms  are  thus  called 
because  in  the  universal  aflBrmative  proposition  (A)  the 
predicate  is  necessarily  a  wider  or  greater  or  major 
term  than  the  subject ;  thus  in  "all  men  are  mortals," 
the  predicate  includes  all  other  animals  as  well  as  men, 
and  is  obviously  a  major  term  or  wider  term  than  men. 

(2)  The  Second  Rule. — The  syllogism  necessarily 
consists  of  a  premise  called  the  major  premise,  in  which 
the  maior  and  middle  terms  are  compared  together ;  of 


LAWS  OF  THOUGHT. 


11? 


a  minor  premise  which  similarly  compares  the  minor 
and  middle  terms ;  and  of  a  conclusion,  which  contains 
the  major  and  minor  terms  only.  In  a  strictly  correct 
syllogism  the  major  premise  always  stands  before  the 
minor  premise,  but  in  ordinary  writing  and  speaking 
this  rule  is  seldom  observed ;  and  that  premise  which 
contains  the  major  term  still  continues  to  be  the  major 
premise,  whatever  may  be  its  position. 

(3)  The  third  rule  is  a  very  important  one,  because 
many  fallacies  arise  from  its  neglect.  By  the  middle 
term  being  distributed  once  at  least,  we  mean  (see  p. 
79)  that  the  whole  of  it  must  be  referred  to  universally 
in  one  premise,  if  not  both.     The  two  propositions — 

All  Frenchmen  are  Europeans, 

All  Russians  are  Europeans, 
do  not  distribute  the  middle  term  at  all,  because  they 
are  both  aflBrmative  propositions,  which  have  (p.  80) 
undistributed  predicates.  It  is  apparent  that  French- 
men are  one  part  of  Europeans,  and  Russians  another 
part,  as  shown  in  Euler's  method  in  Fig.  6,  so  that 

Pig.  6. 


there  is  no  real  middle  term.    Those  propositions  would 
equally  allow  of  Russians  being  or  not  being  French- 


118  SYLLOGISMS. 

men ;  for  whether  the  two  interior  circles  overlap  or 
not  they  are  equally  within  the  larger  circle  of  Euro- 
peans.    Again,  the  two  propositions 

All  Frenchmen  are  Europeans, 
All  Parisians  are  Europeans, 

do  not  enable  us  to  infer  that  all  Parisians  are  French- 
men.    For  though  we  know  of  course  that  all  Parisians 

Pig.  7. 


are  included  among  Frenchmen,  the  premises  would 
allow  of  their  being  placed  anywhere  within  the  circle 
of  Europeans.  We  see  in  this  instance  that  the  prem- 
ises and  conclusion  of  an  apparent  argument  may  all  be 
true  and  yet  the  argument  may  be  fallacious 

The  part  of  the  third  rule  which  refers  to  an  ambiguous  middle 
term  hardly  requires  explanation.  It  has  been  stated  (Chap.  I, 
Sect.  2.)  that  an  ambiguou-s  term  ia  one  which  has  two  different 
meanings,  implying  different  connotations,  and  it  is  really  equiv- 
alent to  two  different  terms  which  happen  to  have  the  same  form 
of  spelling,  so  that  they  are  readily  mistaken  for  each  other. 
Thus  if  we  were  to  argue  that  because  "all  metals  are  elements 
and  brass  is  metal,  therefore  it  is  an  element,"  we  should  be 
committing  a  fallacy  by  using  the  middle  term  metal  in  two  dif- 


LAWS  OF  THOUGHT.  119 

ferent  senses,  in  one  of  which  it  means  tlie  pure  simple  sub- 
stances known  to  chemists  as  metals,  and  in  the  other  a  mixture 
of  metals  commonly  called  metal  in  the  arts,  but  known  to 
chemists  by  the  name  alloy.  In  many  examples  which  may  be 
found  in  logical  books  the  ambiguity  of  the  middle  term  is  ex- 
ceedingly obvious,  but  the  reader  should  always  be  prepared  to 
meet  with  cases  where  exceedingly  subtle  and  difficult  cases  of 
ambiguity  occur.  Thus  it  might  be  argued  that  "  what  is  right 
should  be  enforced  by  law,  and  that  charity  is  right  and  should 
therefore  be  enforced  by  the  law."  Here  it  is  evident  that  right 
is  applied  in  one  case  to  what  the  conscience  approves,  and  in  an- 
other case  to  what  public  opinion  holds  to  be  necessary  for  the 
good  of  society. 

(4)  The  fourth  rule  forbids  us  to  distribute  a  term  in 
the  conclusion  unless  it  was  distributed  in  the  premises. 
As  the  sole  object  of  the  syllogism  is  to  prove  the  con- 
clusion by  the  premises,  it  is  obvious  that  we  must  not 
make  a  statement  concerning  anything  unless  that 
thing  was  mentioned  in  the  premises,  in  a  way  warrant- 
ing the  statement.  Thus  if  we  were  to  argue  that 
"  because  many  nations  are  capable  of  self-government 
and  tliat  nations  capable  of  self-government  sliould  not 
receive  laws  from  a  despotic  government,  therefore  no 
nation  should  receive  laws  from  a  despotic  govern- 
ment," we  should  be  clearly  exceeding  the  contents  of 
oui-  premises.  The  minor  term,  many  nations,  was 
particular  in  the  minor  premise,  and  must  not  be  made 
universal  in  the  conclusion.  The  premises  do  not. 
warrant  a  statement  concerning  anything  but  the  many 
nations  capable  of  self-government.  The  above  argu- 
ment would  therefore  be  fallacious  and  would  be  tech- 
nically called  an  illicit  process  of  the  minor  term,  mean- 
ing that  we  have  improperly  treated  the  minor  term. 


120  SYLLOGISMS. 

Such  a  breach  of  the  fourth  rule  as  is  described  above 
is  exceedingly  easy  to  detect,  and  is  therefore  very  sel- 
dom committed. 

But  an  illicit  process  or  improper  treatment  of  the 
major  term  is  more  common  because  it  is  not  so  trans- 
parently false.  If  we  argued  indeed  that  ''because  all 
Anglo-Saxons  love  liberty,  and  Frenchmen  are  not 
Anglo-Saxons,  therefore  they  do  not  love  liberty,"  the 
fallacy  would  be  pretty  apparent;  but  without  a  knowl- 
edge of  logic  it  would  not  be  easy  to  give  a  clear  ex- 
planation of  the  fallacy.  It  is  apparent  that  the  major 
term  loving  liberty,  is  undistributed  in  the  major  prem- 
ise, so  that  Anglo-Saxons  must  be  assumed  to  be  only  a 
part  of  those  who  love  liberty.  Hence  the  exclusion 
of  Frenchmen  from  the  class  Anglo-Saxons  does  not 
necessarily  exclude  them  from  the  class  who  love  liberty 
(see  Fig.  8).     The  conclusion  of  the  false  argument 

Pio.  8. 


Lovitig  Liberty 

AngU.   i^^Jj 
Saxons    /    \__^/ 


being  negative  distributes  its  predicate,  the  major  term, 
and  as  this  is  undistributed  in  the  major  premise  we 
have  an  illicit  major,  as  we  may  briefly  call  this  fal- 
lacy. 


LAWS  OF  THOUGHT.  121 

The  following  is  an  obscurer  example  of  the  same  fallacy  :— 
"Few  students  are  capable  of  excelling  in  many  branches  of 
knowledge,  and  such  as  can  so  excel  are  deserving  of  high  com- 
mendation;" hence,  "few  students  are  deserving  of  high  com- 
mendation." The  little  word  "  few  "  has  here  the  double  mean< 
ing  before  explained  (p.  71),  and  means  that  "  a  few  are,  etc.,  and 
the  rest  are  not."  The  conclusion  is  thus  really  a  negative  prop- 
osition, and  distributes  the  major  term  "deserving  of  high  com- 
mendation." But  this  major  term  is  clearly  undistributed  in  the 
major  premise,  which  merely  asserts  that  those  who  can  excel  in 
many  branches  of  knowledge  are  deserving,  but  says  or  implies 
nothing  about  other  students. 

(5)  The  fifth  rule  is  evidently  founded  on  the  prin- 
ciple noticed  in  the  last  lesson,  that  inference  can  only 
proceed  where  there  is  agreement,  and  that  two  differ- 
ences or  disagreements  allow  of  no  reasoning.  Two 
terms,  as  the  third  Canon  states,  may  both  differ  from 
a  common  term  and  yet  may  or  may  not  differ  from 
each  other.     Thus  if  we  were  to  argue  that  Americans 

Fig.  9. 


are  not  Europeans,  and  Virginians  are  not  Europeans, 
we  see  that  both  terms  disagree  with  the  middle  term 
6 


123  SYLLOGISMS. 

Europeans,  and  yet  they  agree  between  themselves.  In 
other  cases  the  two  negative  premises  may  be  plainly 
true  while  it  will  be  quite  uncertain  whether  the  major 
and  minor  terms  agree  or  not.  Thus  it  is  true,  for 
instance,  that  "  Colonists  are  not  Europeans  and  Amer- 
icans are  not  Europeans,"  but  this  gives  us  no  right  to 
infer  that  Colonists  are  or  are  not  Americans.  The 
two  negative  premises  are  represented  in  Fig.  9,  by  ex- 
cluding the  circles  of  Colonists  and  Americans  from 
that  of  Europeans ;  but  this  exclusion  may  still  be 
effected  whether  Colonists  and  Americans  coincide  par- 
tially, or  wholly,  or  not  at  all.  A  breach  of  this  rule 
of  the  syllogism  may  be  conveniently  called  the  fallacy 
of  negative  premises.  It  must  not,  however,  be  sup- 
posed that  the  mere  occurrence  of  a  negative  particle  (not 
or  no)  in  a  proposition  renders  it  negative  in  the  man- 
ner contemplated  by  this  rule.     Thus  the  argument 

"  What  is  not  compound  is  an  element. 

Gold  is  not  compound  ; 

Therefore  Gold  is  an  element,'* 
contains  negatives  in  both  premises,  but  is  nevertheless 
valid,  because  the  negative  in  both  cases  affects   the 
middle  term,  which  is  really  the  negative  term  not-com- 
pound. 

(6)  The  sixth  rule. — The  truth  of  the  sixth  rule 
depends  upon  that  of  the  axiom,  that  if  two  terms 
agree  with  a  common  third  term  they  agree  with  each 
other,  whence,  remembering  that  a  negative  proposi- 
tion asserts  disagreement,  it  is  evident  that  a  negative 
conchision  could  not  be  drawn  from  really  affirmative 
premises.  The  corresponding  negative  axiom  prevents 
our  drawing  an  affirmative  conclusion  if  either  premise 


LAWS   OF  THOUGHT.  123 

should  be  really  negative.  Only  practice,  however,  will 
enable  the  student  to  apply  this  and  the  preceding 
rules  of  the  syllogism  with  certainty,  since  fallacy  may 
be  hidden  and  disguised  by  various  forms  of  expression. 
Numerous  examples  are  given  at  the  end  of  the  book  by 
which  the  student  may  acquire  facility  in  the  analysis 
of  arguments. 

The  remaining  rules  of  the  syllogism,  the  7th  and  8th, 
are  by  no  means  of  a  self-evident  character  and  are  in 
fact  corollaries  of  the  first  six  rules,  that  is  consequences 
which  follow  from  them.  We  shall  therefore  have  to 
show  farther  on  that  they  are  true  consequences.  We 
may  call  a  breach  of  the  7th  rule  :^  fallacy  of  particular 
premises,  and  that  of  the  8th  rule  the  fallacy  of  a  uni- 
versal  conclusion  from  a  particular  premise,  but  these 
fallacies  may  really  be  resolved  into  those  of  Illicit  Pro- 
cess, or  Undistributed  Middle. 

For  many  details  concerning  the  Aristotelian  and 
Scholastic  Views  of  the  Syllogism,  and  of  Formal 
Logic  generally,  see  the  copious  critical  notes  to 
Hansel's  edition  of  Aldrich's  Artis  LogiccB  Rudi- 
menta.    Second  Edition.     Oxford.     1852. 

In  this  section,  on  "The  Rules  of  the  Syllo- 
sfism,*'  we  have  considered  : — 

1.  TJie  Definition  of  Si/llogistn." 

2.  TJie  Meaning  of  '*  Middle  Term.'* 

3.  The  Use  of  Middle  Term  in  Syllogism. 

4.  The  Statement  of  the  Btdes  of  the  Syllogism. 

5.  TJie  Explanation  of  the  Mules  of  the  Syllo- 
gism.. 


124  SYLLOGISMS. 


SECTION   in. 

THE   MOODS  AND   FIGURES  OF  THE  SYLLO- 
GISM. 

1.  Explanation  of  "Moods." 

We  are  now  in  full  possession  of  those  principles  oi 
reasoning,  and  the  rules  founded  upon  them,  by  which 
a  true  syllogism  may  be  known  from  one  which  only 
seems  to  be  a  true  one,  and  our  taak  in  the  present  sec- 
tion is  to  ascertain  the  various  shapes  or  fashions  in 
which  a  jirocess  of  mediate  inference  or  syllogism  maj 
be  met  with.  We  know  that  every  syllogistic  argument 
must  contain  three  propositions  and  three  distinct  terms 
each  occurring  twice  in  those  propositions.  Each  prop- 
osition of  the  syllogism  may,  so  far  as  we  yet  know,  be 
either  affirmative  or  negative,  universal  or  particular, 
so  that  it  is  not  difficult  to  calculate  the  utmost  possible 
number  of  modes  in  which  a  syllogism  might  conceiv- 
ably be  constructed.  Any  one  of  the  four  propositions 
A,  E,  I,  or  O  may  in  short  be  taken  as  a  major  premise, 
and  joined  with  any  one  of  the  same  form  as  a  minor 
premise,  and  any  one  of  the  four  again  may  be  added 
as  conclusion.  We  should  thus  obtain  a  series  of  the 
combinations  or  modes  of  joining  the  letters  A,  E,  I,  O, 
a  few  of  which  are  here  written  out : 


AAA 

AEA 

AIA 

AOA 

EAA 

EEA 

AAE 

AEE 

AIE 

AOE 

EAE 

EEE 

AAI 

AEI 

All 

AOI 

EAI 

EEI 

AAO 

AEO 

AIO 

AOO 

EAO 

Ac. 

[t  is  obvious  that  there  will  be  altogether  4  x  4  x  4  or  64 


MOODS  AND    FIGUBB8.  125 

sncli  combinations,  of  which  "Z'i  only  are  given  above. 
The  student  can  easily  write  out  the  remainder  by 
carrying  on  the  same  systematic  changes  of  the  letters. 
Thus  beginning  with  AAA  we  change  the  right-hand 
letter  successively  into  E,  I,  and  0,  and  then  do  the 
same,  beginning  with  AEA  instead ;  after  the  middle 
letter  has  been  carried  through  all  its  changes  we  begin 
to  change  the  left-hand  letter.  With  each  change  of 
this  we  have  to  repeat  all  the  sixteen  changes  of  the 
other  letters,  so  that  there  will  obviously  be  altogether 
64diflf'erent  conceivable  modes  of  arranging  propositions 
into  syllogisms.  We  call  each  of  these  triplets  of  prop- 
ositions a  mood  or  form  of  the  syllogism  (Latin  moausy 
shape). 

2.  The  Number  of  Valid  Moods. 

We  have  to  consider  how  many  of  such  forms  car. 
really  be  used  in  valid  arguments,  as  distinguished  from 
those  which  break  one  or  more  of  the  rules  of  the  syllo- 
gism. Thus  the  mood  AEA  would  break  the  6th  rule, 
that  if  one  premise  be  negative  the  conclusion  must  be 
so  too;  AIE  breaks  the  converse  part  of  the  same  rule, 
that  a  negative  conclusion  can  only  be  proved  by  a 
negative  premise  ;  while  EEA,  EEE,  etc.,  break  the  5th 
rule,  which  prohibits  our  reasoning  at  all  from  two 
negative  premises.  Examples  of  any  of  these  moods 
can  easily  be  invented,  and  their  falsity  would  be  very 
apparent;  thus  for  AEA  we  might  take 

All  Austrians  are  Europeans, 
No  Australians  are  Europeans ; 
Therefore,  all  Australians  are  Austrians. 


126  SYLLOGISMS. 

Many  of  the  64  conceivable  moods  are  excluded  by  the 
7th  and  8th  rules  of  the  syllogism.  Thus  AIA  and  EIE 
break  the  rule,  that  if  one  premise  be  particular  the 
conclusion  must  be  so  also,  while  HA,  100,  010  and 
many  others,  break  the  rule  against  two  particular 
premises.  Some  combinations  of  propositions  may  break 
more  than  one  rule ;  thus  000  has  both  negative 
premises  and  particular  premises,  and  OOA  also  violates 
as  well  the  Gth  rule.  It  is  an  admirable  exercise  in  the 
use  of  the  syllogistic  rules  to  write  out  all  the  64  com- 
binations and  then  strike  out  such  as  break  any  rule ; 
the  task,  if  pursued  systematically,  will  not  be  so  long 
or  tedious  as  might  seem  likely.  It  will  be  found  that 
there  are  only  twelve  moods  which  escape  exclusion, 
and  may  so  far  be  considered  good  forms  of  reasoning, 
and  these  are 

AAA        EAE        lAI        OAO 

AAI         EAO      (lEO) 

AEE       EIO 

AEO 

AU 

AOO 

Of  these,  however,  lEO  will  have  shortly  to  be  rejectea, 
because  it  will  be  found  really  to  break  the  4th  rule, 
and  involves  illicit  process  of  the  major  term.  There 
are,  then,  only  eleven  moods  of  the  syllogism  which  are 
really  valid  ;  and  we  may  tV  as  account  for  the  whole  of 
the  sixty-four  moods. 

No.  of 
Excluded  by  Moodi 

Negative  premises,  Rule  5 16 

Particalar  premises,  "      7 12 

One  negative  premise,       "      6 12 

One  premise  particular,    "      8 8 


MOODS   AJfD   FIGURES.  127 

No.  af 
Excluded  by  Mooda. 

Negative  conclusion.  Rule  6 4 

Illicit  major  *'     4 1 

Total  excluded 53 

Valid  moods 11 

Total 64 


3.  Explanation  of  **  Figures." 

We  have  by  no  means  exhausted  as  yet  all  the  pos- 
sible varieties  of  the  syllogism,  for  we  have  only  deter- 
mined the  character,  affirmative  or  negative,  general  or 
particular  of  the  propositions,  but  have  not  decided  the 
ways  in  which  the  terms  may  be  disposed  in  them. 
The  major  term  must  be  the  predicate  of  the  conclusion, 
but  it  may  either  be  subject  or  predicate  of  the  major 
premise,  and  similarly  the  minor  term  or  subject  of  the 
conclusion,  may  be  either  the  subject  or  predicate  of 
the  minor  premise.  There  thus  arise  four  different 
ways,  or  as  they  are  called  Figures,  in  which  the  terms 
can  be  disposed.  These  four  figures  of  the  syllogism 
are  shown  in  the  following  scheme,  taking 

X  to  denote  the  major    term 

Y middle    « 

Z minor      " 


Fig.  1. 

Fig.  2. 

Pig.  3. 

Pig.  4. 

Major  Premise 

YX 

XY 

YX 

XY 

Minor        " 

Z  Y 

Z  Y 

Y  Z 

Y  Z 

Conclusion 

Z  X 

Z  X 

Z  X 

Z  X 

These  figures  must  be  carefully  committed  to  memory, 
which  will  best  be  done  by  noting  the  position  of  tha 


128  SYLLOGISMS. 

middle  term,  This  term  stands  first  as  subject  of  the 
major  premise  in  the  1st  Figure,  second  as  predicato  in 
both  premises  of  the  2d  Figure,  first  again  as  subiecl 
of  both  premises  in  the  3d  Figure,  and  in  an  inter- 
mediate position  in  the  4th  Figure.  In  the  conclusion, 
of  course,  the  major  and  minor  terms  have  one  fixed 
position,  and  when  the  middle  term  is  once  correctly 
placed  in  any  figure  we  easily  complete  the  syllogism. 

The  reader  will  hardly  be  pleased  to  hear  that  each  of  the 
eleven  valid  moods  will  have  to  be  examined  in  each  of  the  four 
figures  separately,  so  that  there  are  44  cases  still  possible,  from 
which  the  valid  syllogisms  have  to  be  selected.  Thus  the  mood 
AEE  in  the  first  figure  would  be  as  follows  : 

All  F's  are  X's, 
No  Z's  are  F's; 
Therefore  No  Z's  are  X'a. 

This  would  break  the  4th  rule  and  be  an  Illicit  Major,  because 
Xis  distributed  in  the  conclusion,  which  is  a  negative  proposi- 
tion, and  not  in  the  major  premise.  In  the  second  figure  it  would 
be  valid; 

All  X's  are  F's, 

No  Z'&  are  T  s; 
Therefore  No  Z'»  are  -X'a. 

In  the  third  figure  it  becomes 

All  F's  are  X's, 

No  F's  are  Z's, 

No  Z's  are  X's, 
and  again  breaks  the  4th  rule,  as  reganls  the  major  term.    Lastly 
In  the  4th  figure  it  is  valid,  as  the  reader  may  nasily  satisfy  him- 
self. 

4.  The  Valid  Moods  in  the  Different  PIgriires. 

When  all  the  valid  moods  are  selected  out  of  tbfi  44 


ilOODS    AND   FIGUKES. 


in 


possible  ones,  there 

are  found  to  be  altogether  24,  whicb 

are  as  follows: 

Valid  Moods  of  the  Sylloqism. 

Rrrt 
Rgura. 

AAA 

Second 
Figure. 

EAE 

Third                Fourth 
Figure.              P'igure. 

AAI            AAI 

EAE 

AEE 

lAI            AEE 

All 

EIO 

All            lAI 

EIO 

AOO 

EAO           EAO 
OAO           EIO 

lAAI] 
[EAO] 

[EAO] 

[AEO] 

EIO 

[AEO] 

Five  of  the  above  moods  are  set  apart  and  enclosed  in  bracketai 
b«cau8e  tbougli  valid  they  are  of  little  or  no  use.    They  are  said 
to  have  a  weakened  conclusion,  because  the  conclusion  is  par- 
ticular  when  a  general  one  might  have  been  drawn.    Thus  AAI, 
in  the  first  figure  is  represented  by  the  example  : 
All  material  substances  gravitate. 
All  metals  are  material  substances , 
Therefore  some  metals  gravitate. 
It  is  apparent  that  the  conclusion  only  states  a  part  ol  the  truth, 
and  that  in  reality  aU  metals  gravitate.    It  is  not  actually  ax 
erroneous  conclusion,   because  it  must  be  carefully  remembered 
(p.  84)  that  the  affirminor  of  a  subaltern  or  particular  proposition 
does  not  deny  the  correaponding  general  proposition.     It  is  quite 
true  that  some  metals  gravitate,  and  it  must  be  true  because  all 
of  them  do  so.    But  when  we  can  as  readily  prove  that  all  do 
gravitate  it  is  desirable  to  adopt  this  conclusion. 

If  we  agree  with  most  logicians  to  overlook  the  existence  of 
the  five  syllogisms  with  weakened  conclusions,  there  will  remain 
nineteen  which  are  at  once  valid  and  useful.  In  the  next  section 
certain  ancient  mnemonic  lines  will  be  furnished  by  which  alone 
it  would  be  possible  for  most  persons  to  carry  in  the  memory 
these  19  combinations  ;  but  the  reader  ^vill  in  the  meantime  b« 
able  to  gather  from  the  statement  of  the  moods  above  the  truth 
of  the  following  remarks  concerning  the  peculiar  character  of 
each  figure  of  the  syllogism. 


130  SYLLOGISMS. 

5.  Conclusions  Proved  In  the  Different  Figures. 

(1)  The  first  figure  is  the  only  one  which  proves  the 
proposition  A,  or  lias  A  for  its  conclusion.  It  is  the 
only  figure,  too,  which  can  prove  any  one  of  the  four 
propositions  A,  E,  I,  0.  As  regards  the  premises,  it  la 
especially  important  to  note  that  the  major  premise  is 
always  universal  (A  or  E),  and  the  minor  premise  aflBr- 
mative  (A  or  I)  :  this  peculiarity  will  be  further  con- 
sidered in  the  next  lesson. 

(2)  The  second  figure  proves  only  negative  conclu- 
sions (E  or  0),  and  the  reason  is  easily  apparent.  As 
the  middle  term  in  this  figure  is  the  predicate  of  both 
premises  it  would  necessarily  be  undistributed  in  both 
premises  if  these  were  affirmatives.  It  follows  that  one 
premise  must  be  negative  and  of  course  one  only,  so 
that  of  the  major  and  minor  terms  one  must  be  in- 
cluded or  excluded  wholly  from  the  middle,  and  the 
other  at  the  same  time  excluded  or  included  at  least 
partially. 

To  illustrate  this  we  m&j  take  X,  T  and  Z  to  represent,  as 
before,  the  major,  middle  and  minor  terms  of  a  syllogism,  and 
the  four  moods  of  this  figure  are  then 

EAE  AEE 

No  X'a  are  F's,  All  X's  are  F's, 

All  Z's  are  F's  ;  THoZ'a  are  T'a ; 

.*.  No  Z'b  are  X'a.  .*.  No  Zs  are  X'a. 

ElO  AOO 

No  X'b  are  F'b,  AH  X's  are  7*8, 

Some  Z'a  are  T'a  ;  Some  Z'a  are  not  F'sj 

8om/>  Za  are  not  X's.  *.  Some  Z'a  are  not  X'a. 


MOODS   AND   FIGURES. 


131 


The  nature  of  the  moods  of  the  second  figure  is  clearlj 
ihowD  in  the  following  figures : 


Pig.  10. 
(Ceeare.) 


Fig.  11. 
(Camestres.) 


It  win  also  be  observed  that  In  the  second  figare  the  minoi 
premise  may  he  any  of  the  four  A,  E,  I,  0, 

(3)  The  third  figure  only  proves  particulars  (I  or  O), 
and  it  always  has  an  affirmative  minor  premise  (A  or  I). 
It  also  contains  the  greatest  number  of  moods,  since  in 
no  case  is  the  conclusion  a  weakened  one. 

(4)  The  fourth  figure  is  usually  considered  nnnatnra' 
and  comparatively  useless,  because  the  same  arguments 
can  be  more  clearly  arranged  in  the  form  of  the  first 
figure,  which  in  some  respects  it  resembles.  Thus  it 
proves  all  the  propositions  except  A,  namely,  E,  I,  0, 
and  its  first  mood  AAI,  is  in  reality  a  weakened  form  ol 


183  SYLLOGISMS. 

AAA  in  the  first  figure.  Many  logicians,  including  in 
recent  times  Sir  W.  Hamilton,  have  rejected  the  use  ol 
this  figure  altogether. 

It  is  evident  that  tbe  several  figures  of  the  syllogisin  possess 
different  characters,  and  logicians  have  thought  that  each  figure 
was  best  suited  for  certain  special  purposes.  A  Qerman  logi* 
cian,  Lambert,  stated  tliese  purposes  concisely,  as  follows : — ■ 
"  The  first  figure  is  suited  to  the  discovery  or  proof  of  the  prop- 
erties of  a  thing;  the  second  to  the  discovery  or  proof  of  the 
distinctions  between  things  ;  the  third  to  the  discovery  or  proof 
of  instances  and  exceptions;  the  fourth  to  the  discovery,  or 
exclusion,  of  the  different  species  of  genus." 

It  may  be  added  that  the  moods  Cesare  and  Camestres  are  often 
used  in  disproving  a  statement,  because  they  give  a  universal 
negative  conclusion,  founded  upon  the  exclusion  of  one  class 
from  another.  Thus  if  any  one  were  still  to  assert  that  light  con- 
sists of  material  particles,  it  might  be  met  by  the  following  syUo- 
gpsm: 

"Material  particles  communicate  impetus  to 
whatever  they  strike, 
light  does  not  communicate  impetus  to 
whatever  it  strikes ; 
Therefore  light  is  not  material  particles." 

The  moods  Baroko  and  Festino  are  less  used,  but  allow  of  a 
f«rticular  conclusion  being  established. 

When  we  wish,  however,  to  establish  objections  or  exceptions 
to  a  general  statement,  which  is  indeed  the  natural  way  of  meet- 
ing it,  we  employ  the  third  figure.  The  statement  that  "all 
metals  are  solids "  would  at  once  be  disproved  by  the  exception 
mercury,  as  follows: 

Mercury  is  not  solid. 

Mercury  is  a  metal ; 

Therefore  some  metal  is  not  solid. 

Were  any  one  to  assert  that  what  is  incomprehensible  cannot 

exist,  we  meet  it  at  once  with  the  argument  that  Infinity  is  in 

comprehensible,  but  that  infinity  certainly  exists,  because  w« 


REDUCTION   OF  SYLLOGISMS.  133 

cannot  otherwise  explain  the  nature  of  a  curve  line,  or  of  a  quan- 
tity varying  continuously  ;  therefore  something  that  is  incompre' 
hensible  exists.  In  this  case  even  one  exception  is  sufficient 
entirely  to  negative  the  proposition,  which  really  meaus  that 
because  a  thing  is  incomprehensible  it  cannot  exist.  But  if  one 
incomprehensible  thing  does  exist,  others  may  also ;  and  all 
authority  is  taken  from  the  statement. 

According  to  the  Aristotelian  system  the  third  figure  must  also 
be  employed  whenever  the  middle  term  is  a  singular  term,  be- 
cause in  Aristotle's  view  of  the  subject  a  singular  term  could  not 
stand  as  the  predicate  of  a  proposition. 

In  this   section,  on  **The  Moods  and  Figures 
of  the  Syllogism,"  we  have  considered  :— 

1.  Tfie  Explanation  of  Moods, 

2.  The  Number  of  Valid  Moods, 

3.  Tlie  Edcplanation  of  Fif/ures. 

4.  The  Valid  Moods  in  the  Different  Figures. 

5.  Conclusions  Proved  in  the  Different  Figures 


SBGTIOIT  lY. 

THE    REDUCTION    OF    SYLLOGISMS. 

1.  The  Mnemonic  Verses. 

In  order  to  facilitate  the  recollection  of  the  nineteen 
valid  and  useful  moods  of  the  syllogism,  logicians  in- 
vented, at  least  six  centuries  ago,  a  most  curious  system 
of  artificial  words,  combined  into  mnemonic  verses, 
which  may  be  readily  committed  to  memory.  This 
device,  however  ingenious,  is  of  a  barbarous  and  wholly 
unscientific  character  ;  but  a  knowledge  of  its  construe- 
tion  and  use  is  still  expected  from  the  student  of  logic, 


184  SYLLOGISMS. 

and  the  verses  are  therefore  given  and  explained  be« 
low 

pj         ^  ( bArbArA,  cElArEnt,  dArll,  fErlOque  pri- 
°^       *  (     oris; 

cs „  o  i  cEsArE,    cAmEstrEs,    fEstluO,    bArOkO 

Ulgure  ^.  -j      ^^j.  fAkOrO),  secuudse ; 

( tertia,  dArAptI,  dIsAmIs,  dAtlsI,  f ElApt- 
Figure  3.  ]      On,  bOkArdO  (or  dOkAmO),  fErlsOn, 
(      habet ;  quarta,  insuper  addit, 

\^-  A  i  brAmAntlp,  cAmEnEs,  dImArls,  fEsApO, 

1  igure  4.  -j      f rEsIsOn. 

The  words  printed  in  ordinary  type  are  real  Iiatin  words,  signi- 
fying  that  four  moods  whose  artificial  names  are  Barbara,  Celarent. 
Darii  and  Perio,  belong  to  the  first  figure  ;  that  four  otheK  be- 
long to  the  second ;  six  more  to  the  third ;  while  the  fourth 
figure  moreover  contains  five  moods.  Each  artificial  name  con- 
tains three  vowels,  which  indicate  the  propositions  forming  a 
valid  m(x>d ;  thus,  OElAr'Ent  signifies  the  mood  of  the  first  figure, 
which  has  E  for  a  major  premise,  A  for  the  minor,  and  E  for  the 
conclusion.  The  artificial  words  altogether  contain  exactly  the 
series  of  combinations  of  vowels  shown  in  the  scheme  for  the 
valid  moods  of  the  syllogism,  excepting  those  in  brackets. 

2.  Explanation  of  the  Mnemonic  Verses. 

These  mnemonic  lines  also  contain  indications  of  the 
mode  in  which  each  mood  of  the  second,  third  and 
fourth  figures  can  be  proved  by  reduction  to  a  corre- 
sponding mood  of  the  first  figure.  Aristotle  looked 
upon  tLe  first  figure  as  a  peculiarly  evident  and  cogent 
form  of  argument,  the  Dictum  de  omni  et  nullo  being 
directly  applicable  to  it,  and  he  therefore  called  it  the 
Perfect  Figure.  The  fourth  figure  was  never  recog- 
nized by  him,  and  it  is  often  called  the  Galenian  figure, 


REDUCTION  OF  SYLLOGISMS.  135 

because  the  celebrated  Galen  is  supposed  to  have  dis- 
covered it.  The  second  and  third  figures  were  known 
to  Aristotle  as  the  Imperfect  Figures,  which  it  was 
necessary  to  reduce  to  the  first  figure  by  certain  conver* 
sions  and  transpositions  of  the  premises,  for  which 
directions  are  to  be  found  in  the  artificial  words.  These 
directions  are  as  follows: 

3  indicates  that  the  proposition  denoted  by  the  pre- 
ceding vowel  is  to  be  converted  simply. 

p  indicates  that  the  proposition  is  to  be  converted  per 
accidens,  or  by  limitation, 

m  indicates  that  the  premises  of  the  syllogism  are  to 
be  transposed,  the  major  being  made  the  minor  of  a 
new  syllogism,  and  the  old  minor  the  new  major.  The 
m  is  derived  from  the  Latin  mutare,  to  change. 

B,  C,  D,  F,  the  initial  consonants  of  the  names,  in- 
dicate the  moods  of  the  first  figure,  which  are  produced 
by  reduction  ;  thus  Cesare,  Camestres  and  Camenes 
are  reducible  to  Celarent,  Darapti,  etc.,  to  Darii,  Fresi- 
son  to  Ferio  and  so  on. 

k  denotes  that  the  mood  must  be  reduced  or  proved 
by  a  distinct  process  called  Indirect  reduction,  or  re- 
ductio  ad  impossihile,  which  will  shortly  be  considered. 

Examples  of  Reduction. 

(1)  Direct  Reduction.— Let  us  now  take  Bome  syllogism,  say 
In  Camestres,  and  follow  the  directions  for  reduction.  Let  the 
example  be 

All  stars  are  self-luminous (1) 

All  planets  are  not  self-luminous (3) 

Therefore  no  planets  are  stars (3) 

The  first  s  in  Camestres  shows  that  we  are  to  convert  simplj 
the  minor  premise.     The  m  instructs  us  to  change  the  order  a 


186  SYLLOGISMS. 

the  premises,  and  the  final  s  to  convert  the  conclusion  simply 
When  all  these  changes  are  made  we  obtain 

No  self-laminous  bodies  are  planets Converse  of  (3) 

All  stars  are  self-luminous (1) 

Therefore  no  stars  are  planets Converse  of  (3) 

This,  it  will  be  found,  is  a  syllogism  in  Celarent,  as  might  be 
Icnown  from  the  initial  C  in  Camestrea. 
As  another  example  let  us  tak«  Fesapo,  for  instance  : 

No  fixed  stars  are  planets. 
All  planets  are  round  bodies: 
Therefore  some  round  bodies  are  not  fixed  stars. 

According  to  the  directions  in  the  name,  we  are  to  convert 
dmply  the  major  premise,  and  bj  limitation  the  minor  premisa 
We  have  then  the  following  syllogism  in  Ferio  : 

No  planets  are  fixed  stars. 
Some  round  bodies  are  planets ; 
Therefore  some  round  bodies  are  not  fixed  stars. 

The  reader  will  easily  apply  the  same  process  of  conversion  or 
transposition  to  the  other  moods,  according  to  the  directions 
contained  in  their  names,  and  the  only  moods  it  will  be  necessary 
to  examine  especially  are  Bramantip,  Baroko  and  Bokarda  As 
\n  example  of  Bramantip  we  may  take : 

All  metals  are  material  substances. 
All  material  substances  are  gravitating  bodies ; 
Therefore  some  gravitating  bodies  are  metals. 
The  name  contains  the  letter  m,  which  instructs  us  to  trans- 
pose the  premi??es,  and  the  letter  p,  which  denotes  conversion  by 
imitation ;  effectinj?  these  changes  we  have: 

All  material  substances  are  gravitating  bodies 
All  metals  are  material  substances ; 
Therefore  some  metals  are  gravitating  bodies. 
This  is  not  a  syllogism  in  Barbara,  as  we  might  have  expected, 
but  is  the  weakened  mood  AAI  of  the  first  figure.     It  is  evident 
that  the  premises  yield  the  conclusion  "  all  metals  are  gravitating 
bodies,"  and  we  most  take  the  letter  p  to  indicate  in  this  mood 


EEDUCTION   OF  SYLLOGISMS.  137 

that  the  conclusion  is  weaker  than  it  might  be.  In  truth  the 
fourth  figure  is  so  imperfect  and  unnatural  in  form,  containing 
nothing  but  ill  arranged  syllogisms,  which  would  have  been 
better  stated  in  the  first  figure,  that  Aristotle,  the  founder  of 
logical  science,  never  allowed  the  existence  of  the  figure  at  alL 
It  is  to  be  regretted  that  so  needless  an  addition  was  made  to  the 
somewhat  complicated  forms  of  tne  syllogism. 

(2)  Indirect  Reduction. — The  moods  Baroko  and  Bokardo  give 
A  good  deal  of  trouble  because  they  cannot  be  reduced  directly  to 
the  first  figure.  To  show  the  mode  of  treating  these  moods  we 
will  take  X,  T,  Z,  to  represent  tlie  major,  middle  and  minor 
terms  of  the  syllogism,  and  Baroko  may  then  be  stated  as  fol 
lows : 

All  X's  are  T's, 
Some  Z's  are  not  T's ; 
Therefore  Some  Z'a  are  not  X's. 

Now  if  we  convert  the  major  premise  by  Contraposition  (p.  89) 
tre  have  "all  not-y's  are  not-X's,"  and,  making  this  the  major 
premise  of  the  syllogism,  we  have 

All  not-  Y's  are  not  X's, 
Some  Z's  are  not  J^'s  ; 
Therefore  Some  Z'a  are  not  X's. 

"Although  both  the  above  premises  appear  to  be  negative,  this 
^s  really  a  valid  syllogism  in  Ferio,  because  two  of  the  negative 
panicles  merely  affect  the  middle  term  (see  p.  1:34).  and  we  have 
therefore  effected  the  reduction  of  the  syllogism. 

Bokardo.  when  similarly  stated,  is  as  follows 
Some  Y'»  are  not  X's, 
All  r's  are  Z's  ; 
Therefore  Some  Z's  are  not  X's. 

To  reduce  this,  convert  the  major  premise  by  negation,  anfl 
;hen  transpose  the  premises.     We  have : 

All  F's  are  Z's, 
Some  not-X's  are  F's , 
Therefore  Gome  not  X's  are  Z's. 

This  conclusion  is  the  converse  by  negation  of  the  former  con 


138  SYLLOGISMS. 

elusion  the  truth  of  which  is  thus  proved  by  reduction  to  a  syllo 
gism  in  Darii. 

Both  these  moods,  Baroko  and  Bokardo,  may,  however,  b» 
proved  by  a  peculiar  process  of  indirect  reduction,  closely  anal* 
ogous  to  the  indirect  proofs  often  employed  by  Euclid  in  Geom- 
etry. This  process  consists  in  supposing  the  conclusion  of  the 
syllogism  to  be  false,  and  its  contradictory  therefore  true,  when 
a  new  syllogism  can  easily  be  constructed  which  leads  to  a  con- 
clusion contradictory  of  one  of  the  original  premises.  Now  it  is 
absurd  in  logic  to  call  in  question  the  truth  of  our  own  premises, 
for  the  very  purpose  of  argument  or  syllogism  is  to  deduce  a  con- 
clusion which  will  be  true  when  the  premises  are  true.  'J'he  syl- 
logism enables  us  to  restate  in  a  new  form  the  information  which 
is  contained  in  the  premises,  just  as  a  machine  may  deliver  to  us 
in  a  new  form  the  material  which  is  put  into  it.  The  machine,  or 
rather  the  maker  of  the  machine,  is  not  responsible  for  the  quality 
of  the  materials  furnished  to  it,  and  similarly  the  logician  is  not 
responsible  in  the  least  for  the  truth  of  his  premises,  but  only 
for  their  correct  treatment.  He  must  treat  them,  if  he  treat  them 
at  all,  as  true ;  and  therefore  a  conclusion  which  requires  the 
falsity  of  one  of  our  premises  is  altogether  absurd. 

To  apply  this  method  We  may  take  Baroko,  as  before: 

All  X's  are  F's (1) 

Some  Z'a  are  not  F's (3) 

Therefore  Some  Z's  are  not  X'& (8) 

If  this  conclusion  be  not  true  then  its  contradictory,  "all  Z*i 
are  X's,"  must  of  necessity  be  regarded  as  true  (page  84). 
Making  this  the  minor  premise  of  a  new  syllogism  with  the 
original  major  premise  we  have : 

All  X'b  are  Z'b (1) 

All  Z's  are  X's contradictory  of  (3) 

Hence        All  Z's  are  F's. 

Now  this  conclusion  in  A,  is  the  contradictory  of  our  old  minor 
premise  in  0,  and  we  must  either  admit  one  of  our  own  premises 
to  be  false  or  allow  that  our  original  conclusion  is  true.  The 
latter  is  of  course  the  alternative  we  choose. 


REDUCTION  OF  SYLLOGISMS.  189 

We  treat  Bokardo  in  a  very  similar  manner : 

Some  Y's  are  not  X'b (1) 

All  r's  are  Z's (2) 

Therefore  Some  Z'a  are  not  X's (3) 

If  this  conclusion  be  not  true,  then  "all  Z'b  are  X'a"  mustbe 
true.    Now  we  can  make  the  syllogism : 

All  Z's  are  X's Contradictory  of  (3) 

All  F's  are  Z'a (2) 

Hence         All  F'a  are  X's. 

Tliis  conclusion  is  the  contradictory  of  (1),  the  original  major 
premise,  and  as  this  cannot  be  allowed,  we  must  either  suppose 
(2)  the  original  minor  premise  to  be  false,  which  is  equally  im- 
possible, or  allow  that  our  original  conclusion  is  true. 

It  will  be  observed  that  in  both  these  cases  of  Indirect  Reduc- 
tion or  Proof  we  use  a  syllogism  in  Barbara,  which  fact  is  indi- 
cated by  the  initial  letters  of  Baroko  and  Bokardo.  The  same 
process  of  Indirect  proof  may  be  applied  to  any  of  the  other 
moods,  but  it  is  not  usual  to  do  so.  as  the  simpler  process  of 
direct  or  as  it  is  often  called  ostensive  reduction  is  sufficient. 

3.  Conclusions  from  Particular  Premises. 

It  will  be  remembered  that  when  in  Section  2  we 
considered  the  rules  of  the  syllogism,  there  were  two 
supplementary  rules,  the  7th  and  8th,  concerning  par- 
ticular premises,  which  were  by  no  means  of  a  self- 
evident  character,  and  which  require  to  be  proved  by 
the  six  more  fundamental  rules.  We  have  now  suffi- 
ciently advanced  to  consider  this  proof  with  advantage. 
The  7th  rule  forbids  us  to  draw  any  conclusion  from 
two  particular  premises;  now  such  premises  must  be 
either  II,  10,  01,  or  00.  Of  these  II  contain  no  dis- 
tributed term  at  all,  so  that  the  3d  rule,  wliich  requires 
the  middle  term  to  be  dtstributed,  must  be  broken. 
The  premises  00  evidently  break  the  5th  rule,  against 


140  SYLLOGISMS. 

negative  premises.  The  conclusion  of  the  pair  10  must 
be  negative  by  the  6th  rule,  because  one  premise  ia 
negative;  the  major  term  therefore  will  be  distributed, 
but  as  the  major  premise  is  a  particular  affirmative  it 
cannot  be  distributed  without  committing  the  fallacy 
of  illicit  process  of  the  major,  against  rule  4.  Lastly, 
the  premises  01  contain  only  one  distributed  term,  the 
predicate  of  the  major  premise.  But  as  the  conclusion 
must  be  negative  by  rule  6th,  the  major  term  must  be 
distributed :  we  ought  to  have  then  in  the  premises  two 
distributed  terms,  one  for  the  middle  term,  the  other 
for  the  major  term ;  l)ut  as  the  premises  contain  only  a 
single  distributed  term,  we  must  commit  the  fallacy 
either  of  undistributed  middle  or  of  illicit  process  of 
the  major  term,  if  we  attempt  to  draw  any  conclusion 
at  all.  We  thus  see  that  in  no  possible  case  can  a  pair 
of  particular  premises  give  a  valid  conclusion. 

The  8th  rule  of  tlie  syllogism  instructs  us  that  if 
one  premise  of  a  syllogism  be  particular  the  conclusion 
must  also  be  particular.  It  can  only  be  shown  to  be 
true  by  going  over  all  the  possible  cases  and  observing 
that  the  six  principal  rules  of  the  syllogism  always  re- 
quire the  conclusion  to  be  particular.  Suppose,  for  in- 
stance, the  premises  are  A  and  I ;  then  they  contain 
only  one  distributed  term,  the  subject  of  A,  and  this  is 
required  for  the  middle  term  by  rule  3.  Hence  the 
minor  term  cannot  be  distributed  without  breaking 
rule  4,  so  that  the  conclusion  must  be  the  proposition  I. 
The  promises  AO  would  contain  two  distributed  terms, 
the  subject  oi  A  and  the  predicate  of  0  ;  but  if  we  were 
to  draw  from  them  the  conclusion  E,  the  major  and 
minor  terms  would  require  to  be  distributed,  so  thai 


IBEEQULAR   AND   COMPOUND  SYLLOGISMS.         141 

the  middle  term  would  remain  undistributed  against 
rule  3.  The  learner  can  easily  prove  the  other  cases 
such  as  El  by  calculating  the  number  of  distributed 
terms  in  a  similar  manner:  it  will  always  be  found  that 
there  are  insufficient  terms  distributed  in  the  premises 
to  allow  of  a  universal  conclusion. 


In  this  section,  on  "The   Reduction  of  Syllo- 
ffisnis,**  we  have  considered : — 

1.  The  Mnemonic  Verses. 

2.  The  Exitlnnation  of  the  Mnenomic  Versef, 

3.  (Conclusions  from  Particular  Premises, 


SECTION   Y. 

IRREGULAR  AND    COMPOUND   SYLLOGISMS. 

1.  The  Irregular  Mode  of  Expressing  Inferences. 

It  may  seem  surprising  that  arguments  which  are 
met  with  in  books  or  conversation  are  seldom  thrown 
into  the  form  of  regular  syllogisms.  Even  if  a  com- 
plete syllogism  be  sometimes  met  with,  it  is  generally 
employed  in  mere  affectation  of  logical  precision.  In 
former  centuries  it  was,  indeed,  the  practice  for  all 
students  at  the  universities  to  take  part  in  public  dis- 
putations, during  which  elaborate  syllogistic  arguments 
were  put  forward  by  one  side  and  confuted  by  precise 
syllogisms  on  the  other  side.  This  practice  has  not 
been  very  long  discontinued  at  the  University  of  Ox- 
ford, and  is  said  to  be  still  maintained  in  some  conti 


142  SYLLOGISMS. 

nental  universities ;  but  except  in  such  school  disputa- 
tions  it  must  be  allowed  that  perfectly  formal  syllo- 
gisms are  seldom  employed. 

In  truth,  however,  It  is  not  syllogistic  arguments  which 
are  wanting;  wherever  any  one  of  the  conjunctions,  there- 
fore, because,  for,  since,  inasmuch  as,  consequently  occurf*,  it  is 
certain  that  an  inference  is  being  drawn,  and  this  will  very  prob- 
ably be  done  by  a  true  syllogism.  It  is  merely  the  complete 
statement  of  the  premises  and  conclusion,  which  is  usually 
neglected  because  the  reader  is  generally  aware  ot  one  or  other 
of  the  premises,  or  he  can  readily  divine  what  is  assumed  ;  and 
it  is  tedious  and  even  offensive  to  state  at  full  length  what  the 
reader  is  already  aware  of.  Thus,  if  I  say  "atmospheric  air 
must  have  weight  because  it  is  a  material  substance,"  I  certainly 
employ  a  syllogism  ;  but  I  think  it  quite  needless  to  state  the 
premise,  of  which  I  clearly  assume  the  truth,  that  "whatever 
is  a  material  substance  has  weight."  The  conclusion  of  tlie 
syllogism  is  the  first  proposition,  viz.,  "atmospheric  air  has 
weight."  The  middle  term  is  "material  substance,"  which  does 
not  occur  in  the  conclusion  ;  the  minor  is  "atmospheric  air,"  and 
the  major,  "having  weight."  The  complete  syllogism  is  evi- 
dently : 

All  material  substances  have  weight, 
Atmospheric  air  is  a  material  substance  ; 
Therefore  atmospheric  air  has  weight. 

This  is  in  the  very  common  and  useful  mood  Barbara. 

2.  Explanation  of  "  Entliynieme." 

A  syllogism  when  incompletely  stated  is  usiuilly  called 
an  enthymeme,  and  this  name  is  often  supposed  to  be 
derived  from  two  Greek  words  (t'l',  in,  and  dvuoq,  mind), 
80  as  to  signify  that  some  knowledge  is  held  by  the 
mind  and  is  supplied  in  the  form  of  a  tacit,  that  is  a 
silent  or  understood  premise.      Most  commonly  this 


IKBEGULAR   AND   COMPOUND   SYLLOGISMS.        143 

will  be  the  major  premise,  and  then  the  enthymeme 
may  be  said  to  be  of  the  First  Order.  Less  commonly 
the  minor  premise  is  unexpressed,  and  the  enthymeme 
is  of  the  Second  Order.  Of  this  nature  is  the  follow- 
ing argument:  ''Comets  must  be  subject  to  the  law  of 
gravitation ;  for  this  is  true  of  all  bodies  which  move  in 
elliptic  orbits."  It  is  so  clearly  implied  that  comets 
move  in  elliptic  orbits,  that  it  would  be  tedious  to  state 
this  as  the  minor  premise  in  a  complete  syllogism  of 
the  mood  Barbara,  thus : 

All  bodies  moving  in  elliptic  orbits  are  subject  to  the 
law  of  gravitation ; 

Comets  move  in  elliptic  orbits ; 

Therefore  comets  are  subject  to  the  law  of  gravita- 
tion. 

It  may  happen  occasionally  that  the  conclusion  of  a 
syllogism  is  left  unexpressed,  and  the  enthymeme  may 
then  be  said  to  belong  to  the  Third  Order.  This  occurs 
in  the  case  of  epigrams  or  other  witty  sayings,  of  which 
the  very  wit  often  consists  in  making  an  unexpressed 
truth  apparent.  Sir  W.  Hamilton  gives  as  an  instance 
of  this  kind  of  enthymeme  the  celebrated  epigram 
written  by  Person  the  English  scholar  upon  a  contem- 
porary German  scholar : 

'•'  The  Germans  in  Greek 
■Are  sadly  to  seek ; 
Not  five  in  five  score. 
But  ninety-five  more  ; 
All,  save  only  Hermann, 
And  Hermann's  a  German." 

It  is  evident  that  while  pretending  to  make  an  excep- 


144  SYLLOGISMS. 

tion  of  Hermann,  the  writer  ingeniously  insinuates 
that  since  he  is  a  German  he  has  not  a  correct  knowl- 
edge of  Greek.  The  wonderful  speech  of  Antony  over 
the  body  of  Caesar,  in  Shakspeare's  greatest  liistorical 
play,  contains  a  series  of  syllogistic  arguments  of  which 
the  conchisions  are  suggested  only. 

Even  a  single  proposition  may  have  a  syiiogistio 
force  if  it  clearly  suggest  to  the  mind  a  second  premise 
which  thus  enables  a  conclusion  to  be  drawn.  The  ex- 
pression of  Home  Tooke,  "  Men  who  have  no  rights 
cannot  justly  complain  of  any  wrongs,"  seems  to  be  a 
case  in  point;  for  there  are  few  j)eople  who  have  not 
felt  wronged  at  some  time  or  other,  and  they  would 
therefore  be  likely  to  aigue,  whether  upon  true  or  false 
premises,  as  follows: 

Men  who  have  no  rights  cannot  justly  complain  of 

any  wrongs ; 
We  can  justly  complain  ; 
Therefore  we  are  not  men  who  have  no  rights. 

In  other  words,  we  have  rights. 

3.  Prosy lIogLsins  and  Episyllogisms. 

Syllogisms  may  be  variously  joined  and  combined 
together,  and  it  is  convenient  to  have  special  names  for 
the  several  parts  of  a  complex  argument  Thus  a  syl- 
logism which  proves  or  furnishes  a  reason  for  one  of 
the  premises  of  another  syllogism  is  called  a  Prosyllo- 
gism  ;  and  a  syllogism  which  contains  as  a  premise  tho 
conclusion  of  another  syllogism  is  culled  an  Episyiio* 
gism. 


IRREGULAR  AND   COMPOUND  SYLLOGISMS.         145 

Take  the  example  : 

All  ^'s  are  ^'s. 
All  (7'8  area's; 
Therefore  all  C's  are  A\ 
But  all  Z>'s  are  O's  ; 
Tlierefore  All  Z)'s  are  ^'s. 

This  evidently  contains  two  syllogisms  in  the  mood 
Barbara,  the  first  of  which  is  a  Prosyllogism  with 
respect  to  the  second,  while  the  second  is  an  Episyllo- 
gism  with  respect  to  the  first. 

The  peculiar  name  Epicheirema  is  given  to  a  syllo- 
gism when  either  premise  is  proved  or  supported  by  a 
reason  implying  the  existence  of  an  imperfectly  en- 
pressed  prosyllogism ;  thus  the  form. 

All  B's  are  A's,  for  they  are  P's, 
And  all  C's  are  B's,  for  they  are  Q's; 
Therefore  all  C's  are  ^'s, 
is  a  double  Epicheirema,  containing  reasons  for  both 
premises.      The  reader  will  readily  decompose  it  into 
three  complete  syllogisms  of  the  mood  Barbara. 

4.  Sorites. 

A  more  interesting  form  of  reasoning  is  found  in  the 
chain  of  syllogisms  commonly  called  the  Sorites,  from 
the  Greek  word  ocopog,  meaning  heap.  It  is  usually 
stated  in  this  way : 

All  ^'s  are  ^'s, 
All  B's  are  C's, 
All  C's  are  D% 
All  Z>'s  are  E's  ; 
Therefore  all  A'a  are  B'b. 


148  SYLLOGISMS. 

The  chain  can  be  carried  on  to  any  length  provided  it 
is  perfectly  consecutive,  so  that  each  term  except  the 
first  and  last  occurs  twice,  once  as  subject  and  once  as 
predicate.  It  hardly  needs  to  be  pointed  out  that  the 
sorites  really  contains  a  series  of  syllogisms  imperfectly 
expressed;  thus 

First  Syllogism.  Second  Syllogism.  Last  Syllogism. 

B'&  are  C's,  C's  are  j9's  ;  i>'s  are  E'&. 

^'s  are  5*8 ;  ^'s  are  (7's;  J's  are  Z)'s; 

.-.  J's  are  C's.  .*.  ^'s  are  Z)'s.  .-.  ^'s  are  .£"8. 

Bach  syllogism  furnishes  a  premise  to  the  succeeding 
one,  of  which  it  is  therefore  the  prosyllogism,  and  any 
syllogism  may  equally  be  considered  the  episyllogism  of 
that  which  precedes. 

In  the  above  sorites  all  the  premises  were  universal 
and  affirmative,  but  a  sorites  may  contain  one  particu- 
lar premise  provided  it  be  the  first,  and  one  negative 
premise  provided  it  be  the  last.  The  learner  may 
easily  assure  himself  by  trial,  that  if  any  premise  except 
the  first  were  particular  the  fallacy  of  undistributed 
middle  would  be  committed,  because  one  of  the  middle 
terms  would  be  the  predicate  of  one  affirmative  premise 
and  the  subject  of  another  particular  premise.  If  any 
premise  but  the  last  were  negative  there  would  be  a 
fallacy  of  illicit  process  of  the  major  term. 

It  is  not  to  be  supposed  that  the  forms  of  the  syllogism 
hitherto  described  are  all  the  kinds  of  reasoning  actually 
employed  in  science  or  common  life  In  addition  to  the  hjpo- 
tbetical  and  disjunctive  syllogisms  and  some  other  forms  to  be 
described  in  succeeding  sections,  there  are  really  mauy  modes  of 
reasoning  of  which  logicians  have  not  taken  much  notice  aa 
^et.     This  w\s  clearly  pointed  oat  more  than  two  hundred  years 


lEREGULAB  AND  COMPOUND  SYLLOGISMS.        147 

ago  by  the  writers  of  the  Port  Royal  Ijogic,  a  work  first  printed 
in  the  year  1662,  but  which  has  since  been  reprinted  very  often, 
and  translated  into  a  great  many  languages.  The  book  is  named 
from  a  place  near  Paris  where  a  small  religious  community  lived, 
of  which  the  authors  of  the  book,  namely  Arnauld  and  Nicole, 
and  a  contributor  to  it  the  jyreat  philosopher  and  mathematician 
Pascal,  were  the  most  celebrated  members.  The  Port  Royal 
Logic  was  to  a  considerable  extent  the  basis  of  the  well-known 
Watts'  Logic,  but  the  reader  can  now  be  referred  to  an  admirable 
translation  of  the  original  work  made  by  Professor  Spencer 
Baynes  of  St.  Andrew's. 

Many  improvements  of  Logic  may  be  found  in  this  work,  such 
as  the  doctrine  of  Extension  and  Intension,  already  explained. 
In  the  Ninth  Chapter  of  the  Third  Part,  moreover,  it  is  wisely 
pointed  out  that  "  little  pains  are  taken  in  applying  the  rules  cf. 
the  syllogism  to  reasonings  of  which  the  propositions  are  com 
plex,  though  this  is  often  very  difficult,  and  there  are  many 
arguments  of  this  nature  which  appear  bad,  but  wliich  are  never, 
theless  very  good ;  and  besides,  the  use  of  such  reasonings  is 
much  more  frequent  than  that  of  syllogisms  which  are  quite 
simple."  Some  examples  are  given  of  the  complex  syllogisms 
here  referred  to ;  thus : 

The  sun  is  a  thing  insensible, 
The  Persians  worship  the  sun ; 

Therefore  the  Persians  worship  a  thing  insensible. 

This  is  an  argument  which  cannot  be  proved  by  the  rules  of 
the  syllogism,  and  yet  it  is  not  only  evidently  true,  but  is  an  ex- 
ceedingly common  kind  of  argument.  Another  example  is  as 
follows : 

The  Divine  Law  commands  us  to  honor  kings ; 

Louis  XIV  is  a  king ; 

Therefore  the  Divine  Law  commands  us  to  honor  Ijouis  XIV. 

The  reader  will  also  find  that  arguments  which  are  really  quite 
valid  and  syllogistic  are  expressed  in  language  so  that  they 
appear  to  have  four  distinct  terms,  and  thus  to  break  one  of  the 
rules  of  the  syllogism.  Thus,  if  I  say  "Diamonds  are  combus- 
tible, for  they  are  composed  of  carbon  and  carbon  is  combustible,' 


148  SYLLOGISMS. 

there  are  four  terms  employed,  namely,  diamonds,  combustible^ 
x>mpo8ed  of  carbon,  and  carbon.  But  it  is  easy  to  alter  the  con- 
dtraction  of  the  propositions  so  as  to  get  a  simple  syllogism  with- 
jut  really  altering  the  sense,  and  we  tlien  have : 

What  is  composed  of  carbon  is  combustible ; 

Diamonds  are  composed  of  carbon  ; 

Therefore  diamonds  are  combustible. 

Examples  are  given  at  the  end  of  the  book  of  concise  argn- 
iOents,  taken  from  Bacon's  Essays  and  other  writings,  which  the 
(Student  can  reduce  to  the  syllogistic  form  by  easy  alterations ; 
•ut  it  should  be  clearly  understood  that  these  changes  are  of  an 
cxtm-logical  character,  and  belong;  more  properly  to  the  science 
of  language.    . 

6^  Syllogisms  in  Extension  and  in  Intension. 

It  may  here  be  explained  that  the  syllogism  and  the 
sorites  can  be  expressed  either  in  the  order  of  exten- 
sion or  that  of  intension.  In  regard  to  the  number  of 
individual  tilings  the  noble  metals  are  part  of  the 
metals,  and  the  metals  are  part  of  the  elements ;  but  in 
regard  to  intension,  that  is  to  say  the  qualities  implied 
in  the  names,  element  is  part  of  metal,  and  metal  is 
part  of  noble  metal.  So  again  in  extension  the  genus 
of  plants  Anemone  is  part  of  the  order  Ranunculaceje, 
and  this  is  part  of  the  great  class  Exogens;  but  in  in- 
tension the  character  of  Exogen  is  part  of  the  character 
of  Ranunculaceae,  and  this  is  part  of  the  character  of 
Anemone.  Syllogistic  reasoning  is  equally  valid  and 
evident  in  either  case,  and  we  might  represent  the  two 
modes  in  ordinary  language  as  follows  : 

Extensive  Syllogism. 
All  Ranuncniacese  are  Exogens ; 
The  Anemone  is  ono  of  the  Rannncu1ace»  ; 
Therefore  the  Anemone  is  an  Exogen. 


CONDITIONAL   SYLLOGISMS.  149 

Intensive  Syllogism. 

All  the  qualities  of  Ranunculacese  are  qualities  of  Anemone , 
All  the  qualities  of  Exogen  are  qualities  of  Ranunculacese ; 
Therefore  all  the  qualities  of  Exogen  are  qualities  of  Anemone 

Any  sorites  can  be  similarly  represented  either  in  extension  or 
Intension. 

Concerning  the  Aristotelian  doctrine  of  the  Enthymeme,  see 
Mansel's  Aldrich,  App.,  Note  F,  and  Hamilton's  Lectures  on 
Logic,  Lecture  XX.  Port  Roynl  Logic,  translated  by  T. 
Spencer  Baynes,  5th  ed.    Edinburgh,  1861. 

In  this  section,  on  "Irregular  and  Compound 
Syllogisms/'  we  have  considered: 

1.  The   Irregular    Mode   of  Expressing    Infer- 
ences. 

2.  The  Eocplanation  of  Enthymeuie, 

3.  Prosy  Hog  istns  and  Episyllogisins. 

4.  Sorites. 

6.  Syllogisms  in  Extension  and  Intension, 


SECTION    YI, 

CONDITIONAL     SYLLOGISMS. 

1.  Classification  of  Propositions. 

It  will  be  remembered  that  when  treating  of  propo- 
sitions we  divided  them  into  two  distinct  kinds,  Cate- 
gorical Propositions,  and  Conditional  Propositions. 
The  former  kind  alone  has  hitherto  been  considered, 
and  we  must  now  proceed  to  describe  Conditional 
propositions  and  the  arguments  which  may  be  com- 
posed of  them. 


150  SYLLOGISMS. 

Logicians  have  commonly  described  Conditional  prop- 
ositions aa  composed  of  two  or  more  Categorical  propo- 
sitions  united  by  a  conjunction.  This  union  may 
happen  in  two  ways,  giving  rise  to  two  very  different 
species  of  conditionals,  which  we  shall  call  Hypothetical 
Propositions  and  Disjunctive  Propositions.  The  way 
in  which  the  several  kinds  of  propositions  are  related 
will  be  seen  in  the  following  diagram : 

i  Categorical, 

2.  Antecedent  and  Consequent. 

A  conditional  proposition  may  be  further  described 
as  one  which  makes  a  statement  under  a  certain  con- 
dition or  qualification  restricting  its  application.  In 
the  hypothetical  form  this  condition  is  introduced  by 
the  conjunction  if,  or  some  other  word  equivalent  to 
it.     Thus— 

"  If  iron  is  impure,  it  is  brittle  '* 

is  a  hypothetical  proposition  consisting  of  two  distinct 
categorical  propositions,  the  first  of  which,  "Iron  is 
impure,"  is  called  the  Antecedent;  the  second,  "It  is 
brittle,"  the  Consequent.  In  this  case  "impurity  "  is 
the  condition  or  qualification  which  limits  the  applica- 
tion of  the  predicate  brittle  to  iron. 

It  was  asserted  by  Home  Tooke  in  his  celebrated  work.  The 
Diversions  of  Purley,  that  all  conjunctions  are  the  remains  or 
corrupted  forms  of  verbs.  This  is  certainly  true  in  the  case  of 
the  hypothetical  conjunction  ;  for  the  word  if  in  old  English  is 
written  gif  or  gyf,  and  is  undoubtedly  derived  from  the  verb  tt 


CONDITIONAL  SYLLOGISMS.  151 

give.  We  may  actually  substitute  at  present  any  verb  of  similar 
meaning,  as  for  instance — grant,  allow,  suppose.  Thus,  we  may 
say — 

"  Grant  that  iron  is  impure,  and  it  is  brittle." 
"  Suppobing  tliat  iron  is  impure,  it  is  brittle." 

3.  Kinds  of  Hypothetical  Syllogisms. 

The  hypothetical  proposition  might  be  employed  in 
arguments  of  various  form,  but  only  two  of  these  are 
of  sufficient  importance  to  receive  special  names.  The 
hypothetical  syllogism  consists  of  two  premises,  called 
the  major  and  minor,  as  in  the  case  of  the  ordinary 
syllogism.  The  major  premise  is  hypothetical  in  form ; 
the  minor  premise  is  categorical,  and  according  as  it  is 
affirmative  or  negative  the  argument  is  said  to  be  a 
Constructive  or  a  Destructive  hypothetical  syllogism. 
Thus  the  form, 

If  A  isB,  CisD; 

But  AisB; 

Therefore  C  is  Z), 
is  a  constructive  hypothetical  syllogism. 

It  must  be  carefully  observed  that  the  minor  premise 
affirms  the  antecedent  of  the  major  premise,  whence 
the  argument  is  said  to  be  of  the  modus  ponens,  or 
mood  which  posits  or  affirms.  It  is  probably  one  of 
the  most  familiar  and  common   kinds  of  argument. 

The  form, 

If  ^  is  5,  C  is  Z> ; 

^ut  C  is  not  D ; 
Therefore  A  is  not  B, 

represents  the  corresponding  Destructive  hypothetical 
syllogism,  also  called  the  modus  tollens,  or  the  mood 
which  removes  the  consequent.     It  must  be  carefully 


152  SYLLOGISMS. 

observed  again  that  it  is  the  consequent,  not  the  ante- 
cedent, which  is  denied. 

4.  The  Rule  for  Hypothetical  Syllogisms. 

The  only  rule  which  is  requisite  for  testing  the 
validity  of  such  syllogisms  embodies  what  we  have 
observed  above,  viz.,  that  either  the  antecedent  must 
be  affirmed,  or  the  consequent  denied.  If  either  part 
of  this  rule  be  broken,  a  serious  fallacy  will  be  com- 
mitted.    Thus  the  apparent  argument. 

If  ^  is^,  CisD; 
Bute  is/); 
Therefore  A  is  B, 

is  really  a  fallacy  which  we  may  call  the  fallacy  of  affirm- 
ing the  consequent,  and  its  fallacious  nature  is  readily 
understood  by  reflecting  that  "  A  being  B"  is  not  stated 
to  be  the  only  condition  on  which  C  is  D.  It  may 
happen  that  when  B  is  F,  or  G  is  H,  or  under  a  hun- 
dred other  circumstances,  C  is  D,  so  that  the  mere  fact 
of  0  being  D  is  no  sufficient  proof  that  A  is  B.  Thus, 
if  a  man's  character  be  avaricious  he  will  refuse  to  give 
money  for  useful  purposes;  but  it  does  not  follow  that 
every  person  who  refuses  to  give  money  for  such  pur- 
poses is  avaricious.  There  may  be  many  proper  reasons 
or  motives  leading  him  to  refuse  ;  he  may  have  no 
money,  or  he  may  consider  the  purpose  not  a  useful 
one,  or  he  may  have  more  useful  purposes  in  view. 

A  corresponding  fallacy  arises  from  denying  the  ante- 
cedent, as  in  the  form — 

U  A  is  B,  C'ls  D; 
But  A  is  not  B  ; 
Therefore  O  is  not  D. 


CONDITIONAL  SYLLOGISMS.  163 

rhe  error  may  be  explained  in  the  same  way;  for  aa 
"A  being  B  "  is  not  stated  to  be  the  only  condition  of 
C  being  D,  we  may  deny  this  one  condition  to  be  true, 
but  it  is  possible  that  the  consequent  may  happen  to  be 
true  for  other  reasons,  of  which  we  know  nothing. 
Thus  if  a  man  is  not  avaricious  we  cannot  conclude 
that  he  will  be  sure  to  give  money  whenever  asked. 
Or  take  the  following  example  : 

*'If  the  study  of  Logic  furnished  the  mind  with  a 
multitude  of  useful  facts  like  the  study  of  other  sciences, 
it  would  deserve  cultivation ;  but  it  does  not  furnish 
the  raind  with  a  multitude  of  useful  facts ;  therefore  it 
iocs  not  deserve  cultivation." 

This  is  evidently  a  fallacious  argument,  because  the 
acquiring  of  a  multitude  of  useful  facts  is  not  the  only 
ground  on  which  the  study  of  a  science  can  be  recom- 
mended. To  correct  and  exercise  the  powers  of  judg- 
ment and  reasoning  is  the  object  for  which  Logic 
deserves  to  be  cultivated,  and  the  existence  of  such 
other  purpose  is  ignored  in  the  above  fallacious  argu- 
ment, which  evidently  involves  the  denial  of  the  ante- 
cedent. 

6.  The  Reduction  of  Hypothetical  to  Categorical 
Syllogisms. 

Although  it  is  usual  in  logical  works  to  describe  the 
hypothetical  proposition  and  syllogism  as  if  they  were 
different  in  nature  from  the  categorical  proposition  and 
syllogism,  yet  it  has  long  been  known  that  the  hypo- 
theticals  can  be  reduced  to  the  categorical  form,  and 
brought  under  the  ordinary  rules  of  the  syllogism.     Aa 


154  8YLLOOISMS. 

a  general  rule  the  hypothetical  proposition  can  hi 
readily  converted  into  a  universal  affirmative  proposi- 
tion (A)  of  exactly  the  same  meaning.  Thus  oui 
instance,  "If  iron  is  impure,  it  is  brittle,"  becomea 
simply,  "Impure  Iron  is  brittle."  In  making  this 
alteration  in  a  hypothetical  syllogism  it  will  be  found 
necessary  to  supply  a  new  minor  term ;  thus  in  the 
case. 

If  iron  is  impure  it  is  brittle ; 

But  it  is  impure  ; 

Therefore  it  is  brittle, 

we  have  to  substitute  for  the  indefinite  pronoun  it,  the 
iron  in  question,  and  we  obtain  a  correct  categorical 
syllogism  in  the  mood  Barbara : 

Impure  iron  is  brittle ; 

The  iron  in  question  is  impure  iron  ; 

Therefore  the  iron  in  question  is  brittle. 

Sometimes  the  reduction  requires  a  more  extensive  change 
•f  language.     For  instance, 

If  the  barometer  is  falling,  bad  weather  is  coming ; 
But  the  barometor  is  falling ; 
Therefore  bad  weather  is  coming, 
may  be  represented  in  the  following  form  : 

The  circumstances  of  the  barometer  falling  are  the  circumstances 

of  bad  weather  coming  ; 
But  these  are  the  circumstances  of  the  barometer  falling ; 
Therefore  these  are  the  circumstances  of  bad  weatlier  coming. 

As  an  instance  of  the  Destructive  Hypothetical  syllogism  wc 
nay  take : 

If  Aristotle  is  right,  slavery  is  a  proper  form  of  societ}* ; 
But  slavery  is  not  a  proper  form  of  society' ; 
Therefore  Aristotle  is  not  right. 


CONDITIONAL  SYLLOGISMS.  165 

Th!ts  becomes  as  a  categorical  - 

The  case  of  Aristotle  being  right  is  the  case  of  slavery  being  a 

proper  form  of  society; 
But  this  is  not  the  case ; 
Therefore  this  is  not  the  case  of  Aristotle  being  right. 

If  not  reducible  by  any  other  form  of  expression,  hypotheticalai 
can  always  be  reduced  by  the  use  of  the  words  case  of. 

6.  Fallacies  in  Hypothetical  Syllogrisms. 

It  will  now  be  easily  made  apparent  that  the  fallacy 
of  afl&rining  the  consequent  is  really  a  breach  of  the 
third  rule  of  the  syllogism,  leading  to  an  undistributed 
middle  term.     Our  example  may  be  as  before  : 

If  a  man  is  avaricious  he  will  refuse  money ; 
But  he  does  refuse  money  ; 
Therefore  he  is  avaricious. 

This  becomes  as  a  categorical  syllogism. 
All  avaricious  men  refuse  money ; 
But  this  man  refuses  money ; 
Therefore  this  man  is  avaricious. 

This  is  the  mood  AAA  in  the  second  figure  ;  and  the 
middle  term,  refusing  money,  is  undistributed  in  both 
premises,  so  that  the  argument  is  entirely  fallacious. 

Again,  the  fallacy  of  denying  the  antecedent  is  equiv- 
alent to  the  illicit  process  of  the  major.  Our  former 
example  (p.  153)  may  thus  be  represented : 

"  A  science  which  furnishes  the  mind  with  a  multi- 
tude of  useful  fact^  deserves  cultivation  ;  but  Logic  is 
not  such  a  science;  therefore  Logic  does  not  deserve 
cultivation." 


156  SYLLOGISMS. 

This  apparent  syllogism  is  of  the  mood  AEE  in  the 
first  figure,  which  breaks  the  fourth  rule  of  the  syllo- 
gism, because  the  major  term,  deservinr/  cultivation,  is 
distributed  in  the  negative  conclusion,  but  not  in  the 
afifirmative  major  premise. 

7.  Di^unctive  Syllogrisms. 

We  now  pass  to  the  consideration  of  the  disjunctive 
proposition,  wiiich  instead  of  a  single  predicate  has 
several  alternatives  united  by  the  disjunctive  conjunc- 
tion or,  any  one  of  which  may  be  affirmed  of  the  subject 
"A  member  of  the  House  of  Commons  is  either  a  repre- 
sentative of  a  county,  or  of  a  borough,  or  of  a  Univer- 
sity," is  an  instance  of  such  a  proposition,  containing 
three  alternatives ;  but  there  may  be  any  number  of 
alternatives  from  two  upwards. 

The  disjunctive  syllogism  consists  of  a  disjunctive 
major  premise  with  a  categorical  proposition,  either 
affirmative  or  negative,  forming  the  minor  premise. 
Thus  arise  two  moods  : 

(1)  The  affirmative  mood  is  called  by  the  Latin  words 
modus  ponendo  tollens  (the  mood  which  by  affirming 
denies),  and  may  be  thus  stated: 

A  is  either  B  or  C, 
But  AisB; 
Therefore  A  is  not  C. 

This  form  of  argumen{  proceeds  on  the  supposition 
that  if  one  alternative  of  a  disjunctive  proposition  be 
held  true,  the  others  cannot  also  be  true.  Thus  "  the 
time  of  year  must  bn  cither  spring,  summer,  autumn  or 
winter,"  and  if  it   be  spring  it  cannot  be  summei; 


CONDITIONAL  SYLLOGISMS.  157 

autumn  or  winter;  and  so  on.  But  it  has  been  ob- 
jected by  Whately,  Mansel,  Mill,  as  well  as  many 
earlier  logicians,  that  this  does  not  always  hold  true. 
Thus  if  we  say  that  "a  good  book  is  valued  either  foi 
the  usefulness  of  its  contents  or  the  excellence  of  its 
style,"  it  does  not  by  any  means  follow  because  the  con- 
tents of  a  book  are  useful  that  its  style  is  not  excel- 
lent. We  generally  choose  alternatives  which  are  in- 
consistent with  each  other ;  but  this  is  not  logically 
necessary. 

(2)  The  other  form  of  disjunctive  syllogism,  called 
the  modus  toilendo  ponens  (the  mood  which  by  deny- 
ing affirms),  is  always  of  necessity  cogent,  and  is  as 
follows: 

A  is  either  B  or  C, 

But  A  is  not  B; 

Therefore  A  is  C. 

Thus  if  we  suppose  a  book  to  be  valued  only  for  the 
usefulness  of  its  contents  or  the  excellence  of  its  style, 
it  follows  that  if  a  book  be  valued,  but  not  for  the 
former  reason,  it  must  be  for  the  latter  ;  and  vice  versa. 
If  the  time  of  year  be  not  spring,  it  must  be  summer, 
autumn  or  winter ;  if  it  be  not  autumn  nor  winter,  it 
must  be  either  spring  or  summer  ;  and  so  on.  In  short 
if  any  alternatives  be  denied,  the  rest  remain  to  be 
affirmed  as  before.  It  will  be  noticed  that  the  disjunc- 
tive syllogism  is  governed  by  totally  different  rules 
from  the  ordinary  categorical  syllogism,  since  a  nega- 
tive premise  gives  an  affirmative  conclusion  in  the 
former,  and  a  negative  conclusion  in  the  latter. 


158  SYLLOGISMS. 

8.  The  Dilemma. 

There  yet  remains  a  form  of  argument  called  the 
Dilemma,  because  it  consists  in  assuming  two  alterna- 
tives, usually  called  the  horns  of  the  dilemma,  and  yet 
proves  something  in  either  case  (Greek,  dt-  two ;  Xfjufia, 
assumption).  Mr.  Mansel  defines  this  argument  as  "a 
syllogism,  having  a  conditional  major  premise  with  more 
than  one  antecedent,  and  a  disjunctive  minor."  Thcro 
are  at  least  three  forms  in  which  it  may  be  stated. 

(1)  The  first  form  is  called  the  Simple  Constructive 
Dilemma : 

If  ^  is  5,  CiaD;  and  if  ^  is  J?;  C is  2>: 
But  either  A  is  B,  or  Bia  F; 
Therefore  C  is  D. 

Thus  *'if  a  science  furnishes  useful  facts,  it  is  worthy 
of  being  cultivated ;  and  if  the  study  of  it  exercises  the 
reasoning  powers,  it  is  worthy  of  being  cultivated  ;  but 
either  a  science  furnishes  useful  facts,  or  its  study  exer- 
cises the  reasoning  powers;  therefore  it  is  worthy  of 
being  cultivated." 

(2)  The  second  form  of  dilemma  is  the  Complex  Con- 
structive Dilemma,  which  is  as  follows: 

IfAisB,CiBD;  and  if  EiaF,  0  is  ff; 
But  either  A  is  B,  or  E  is  F; 
Therefore  either  C  is  D,  or  G  is  H. 

It  is  called  complex  because  the  conclusion  is  in  the 
disjunctive  form.  As  an  instance  we  may  take  the 
argument,  **  If  a  statesman  who  sees  his  former  opinions 
to  be  wrong  doe^  not  alter  his  course,  he  is  guilty  of 
deceit;  and  if  he  does  alter  his  course,  he  is  open  to  a 


CONDITIONAL  SYLLOGISMS.  169 

charge  of  inconsistency ;  but  either  he  does  not  alter 
his  course,  or  he  does  ;  therefore  he  is  either  guilty  of 
deceit,  or  he  is  open  to  a  charge  of  inconsistency."  In 
this  case,  as  in  the  greater  number  of  dilemmas,  the 
terms  A,  B,  0,  B,  etc.,  are  not  all  different, 

(3)  The  Destructive  Dilemma  is  always  complex,  bC" 
cause  it  could  otherwise  be  resolved  into  two  uncon- 
nected destructive  hypothetical  syllogisms.  It  is  in  the 
following  form : 

If  ^  is  5,  OiaD;  and  if  ^ is  i^,  G'  is  ^; 
But  either  0  is  not  D,  or  G  is  no^.  ff ; 
Therefore  either  A  is  not  B,  or  B  is  not  P. 

For  instance,  "  If  this  man  were  wise,  he  would  not 
speak  irreverently  of  Scripture  in  jest ;  and  if  he  were 
good,  he  would  not  do  so  in  earnest ;  but  he  does  it 
either  in  jest  or  earnest ;  therefore  he  is  either  not  wise, 
or  not  good,"  * 

Dilemmatic  arguments  are,  however,  more  often  fallacious 
than  not,  because  it  is  seldom  possible  to  find  instances  where 
two  alternatives  exhaust  all  the  possible  cases,  unless  indeed  one 
of  them  be  the  simple  negative  of  the  other  m  accordance  with 
the  law  of  excluded  middle.  Thus  if  we  were  to  argue  that  "  if 
ft  pupil  is  fond  of  learning  he  needs  no  stimulus,  and  that  if  he 
dislikes  learning  no  stimulus  will  be  of  any  avail,  but  as  he  is 
either  fond  of  learning  or  dislikes  it,  a  stimulus  is  either  needless 
or  of  no  avail,"  we  evidently  assume  improperly  the  disjunctive 
minor  premise.  Fondness  and  dislike  are  not  the  only  two  pos- 
sible alternatives,  for  there  may  be  some  who  are  neither  fond  of 
learning  nor  dislike  it,  and  to  these  a  stimulus  in  the  shape  of 
rewards  may  be  desirable.     Almost  anything  can  be  proved  if  wa 

*  Wh«teu 


160  SYLLOGISMS. 

are  allowed  thus  to   pick  out  two  oi  the  iK>ssible  altemativev 
which  are  ia  our  favor,  and  argue  from  these  alone. 

A  dUemma  can  often  be  retorted  by  producing  as  cogent  a 
dilemma  to  the  contrary  effect.  Thus  an  Athenian  mother,  ac- 
cording to  Aristotle,  addressed  her  son  in  the  following  words; 
"Do  not  enter  into  public  business;  for  if  you  say  what  is  just, 
men  will  hate  you ;  and  if  you  siiy  what  is  unjust  the  gods  will 
hate  you."  To  which  Aristotle  suggests  the  following  retort  •  "J 
ought  to  enter  into  public  affairs  ;  for  if  I  say  what  is  just,  th« 
gods  will  love  me ;  and  if  I  say  what  is  unjust,  men  will  lov* 
me." 

Mansel's  Aldrich,  App.  Note  1,  on  the  Hypothetical  Syllogism 

In  this  section,  on  "Conditional  Syllogisms, *^ 
we  have  considered: — 

1.  The  Classification  of  Propositions, 

2.  Antecedent  and  Consequetit. 

3.  The  Kinds  of  Hypotheticfil  Syllogisms. 
4*  The  Rale  for  Hypothetical  Syllogisms, 

6.  The  Rednction  of  Hypothetical  Syllogism*  #l 

Categorical  Syllogistns. 
O.  Fallacies  in  HypothetictjU  SyUogiawhs, 

7.  Disjunctive  Syllogising, 
8>    T/h}  J>ilemmii, 


CHAPTER    !V. 

FALLACIES. 

In  order  to  acquire  a  satisfactory  knowledge  of  the 
rules  of  correct  thinking,  it  is  essential  that  we  should 
become  acquainted  with  the  most  common  kinds  of 
fallacy;  that  is  to  say,  the  modes  in  which,  by  neglect- 
ing the  rules  of  logic,  we  often  fall  into  erroneous 
reasoning.  In  previous  lessons  we  have  considered,  as 
it  were,  how  to  find  the  right  road  ;  it  is  our  task  here 
to  ascertain  the  turnings  at  which  we  are  most  liable  to 
take  the  wrong  road. 

In  describing  the  fallacies,  I  shall  follow  the  order 
and  adopt  the  mode  of  classification  which  has  been 
usual  for  the  last  2000  years  and  more,  since  in  fact 
the  great  teacher  Aristotle  first  explained  the  fallacies. 
According  to  this  mode  of  arrangement  fallacies  are 
divided  into  two  principal  groups,  containing  the  logi- 
cal and  the  materinl  fallacies. 

1.  The  logical  fallacies  are  those  which  occur  in  the 
mere  form  of  the  statement;  or,  as  it  is  said  in  the  old 
Latin  expressions,  in  dictione,  or  in  voce.  It  is  supposed 
accordingly  that  fallacies  of  this  kind  can  be  discovered 
without  a  knowledge  of  the  subject-matter  with  which 
the  ai'gument  is  concerned. 

2.  The  material  fallacies,  on  the  contrary,  arise  out- 
side of  the  mere  verbal  statement,  or,  as  it  is  said,  extra 
dictionem;  they  are  concerned  consequently,  with  the 


163  FALLACIES. 

subject  of  the  argument,  or  in  re  (in  the  matter),  and 
cannot  be  detected  and  set  right  but  by  those  acquainted 
with  the  subject. 

These  two  classes  of  fallacies  will  now  be  considered 
in  the  following  sections;  (1)  Logical  Fallacies ^ 
(2)  Material  Fallacies, 


8BGTI0IT   !• 
LOGICAL  FALUCIES. 

Ic  Classification  of  Logical  Fallacies. 

The  1 5gical  fallacies  may  be  divided  into  the  purely 
fogical  and  semi-logical,  and  we  may  include  in  the 
former  class  the  distinct  breaches  of  the  syllogistic 
rules  which  have  already  been  described. 

(1)  We  may  enumerate  as  Purely  Logical  Fallacies : 

1.  Fallacy  of  four  terras  {Quaternio  Terminorum) — 
Breach  of  Rule  1 ; 

2.  Fallacy  of  undistributed  middle — Breach  of  Rule  3 ; 

3.  Fallacy  of  illicit  process,  of  the  major  or  minor 
term — Breach  of  Rule  4 ; 

4.  Fallacy  of  negative  premises — Breach  of  Rule  5  ; 
as  well  as  breaches  of  the  6th  rule,  to  which  no  distinct 
name  has  been  given.     Breaches  of  the  7th  and  8th 
mles  may  be  resolved  into  the  preceding  (p.  140),  but 
they  may  also  be  described  as  in  p.  123. 

(2)  The  other  part  of  the  class  of  logical  fallacies  con- 
rains  Semi-logical  fallacies,  which  are  six  in  number 
as  follows : 


LOGICAL   FALLACIES.  168 

1.  Fallacy  of  Equivocation. 

2.  Fallacy  of  Amphibology. 
8.  Fallacy  of  Composition. 

4.  Fallacy  of  Division. 

5.  Fallacy  of  Accent. 

6.  Fallacy  of  Figure  of  Speech. 

0 

These  I  shall  describe  and  illustrate  in  sucoessioiL 

2.  The  Fallacy  of  Equivocation. 

Equivocation  consists  in  the  same  term  being  used  in 
two  distinct  senses ;  any  of  the  three  terms  of  the  syllo- 
gism may  be  subject  to  this  fallacy,  but  it  is  usually  the 
middle  term  which  is  used  in  one  sense  in  one  premise 
and  in  another  sense  in  the  other.  In  this  case  it  ii 
often  called  the  fallacy  of  ambiguous  middle,  and  when 
we  distinguish  the  two  meanings  by  using  other  suitable 
modes  of  expression  it  becomes  apparent  that  the  sup- 
posed syllogism  contains  four  terms.  The  fallacy  of 
equivocation  may  accordingly  be  considered  a  disguised 
fallacy  of  four  terms.  Thus  if  a  person  were  to  argue 
that  "all  criminal  actions  ought  to  be  punished  by  law* 
prosecutions  for  theft  are  criminal  actions ;  thereforf 
prosecutions  for  theft  ought  to  be  punished  by  law,** 
it  is  quite  apparent  that  the  term  "criminal  action*' 
means  totally  different  things  in  the  two  premises,  and 
that  there  is  no  true  middle  term  at  all.  Often,  how- 
ever, the  ambiguity  is  of  a  subtle  and  difficult  character, 
80  that  different  opinions  may  be  held  concerning  it 
Thus  we  might  argue : 

"He  who  harms  another  should  be  punished.  H* 
who  communicates  an  infectious  disease  to  another  per- 


164  PALLAOIBS. 

Bon  harms  him.  Therefore  he  who  communicates  an 
infectious  disease  to  another  person  should  be  pun- 
ished.'* 

This  may  or  .may  not  be  held  to  be  a  correct  argu- 
ment according  to  the  kinds  of  actions  we  should  con- 
sider to  come  under  the  term  harm,  according  as  we 
regard  negUgence  or  malice  requisite  to  constitute  harm. 
Many  difficult  legal  questions  are  of  this  nature,  as,  for 
\nstance : 

Nuisances  are  punishable  by  law  ; 

To  keep  a  noisy  dog  is  a  nuisance; 

To  keep  a  noisy  dog  is  punishable  by  law. 

The  question  here  would  turn  upon  the  degree  of 
nuisance  which  the  law  would  interfere  to  prevent.  Or 
again: 

Interference  with  another  man's  business  is  illegal ; 

Underselling  interferes  with  another  man's  business ; 
Therefore  underselling  is  illegal. 

Here  the  question  turns  upon  the  kind  of  interference, 
and  it  is  obvious  that  underselliog  is  not  the  kind  of 
interference  referred  to  in  the  major  premise. 

3.  The  Fallacy  of  Amphibologry. 

The  Fallacy  of  Amphibology  consists  in  an  ambiguous 
grammatical  structure  of  a  sentence,  which  produces 
misconception.  A  celebrated  instance  occurs  in  the 
prophecy  of  the  spirit  in  Shakspeare's  Henri/  VI. : 
"  The  Duke  yet  lives  that  Henry  shall  depose,"  which 
leaves  it  wholly  doubtful  whether  the  Duke  shall  depose 
Henry,  or  Henry  the  Duke.  This  prophecy  is  doubt- 
less an  imitation  of  those  which  the  ancient  oracle  of 


LOGICAL  FALLACIES.  16ft 

Delphi  is  reported  to  have  uttered  ;  and  it  seems  that 
this  fallacy  was  a  great  resource  to  the  oracles  wlio  were 
not  confident  in  their  own  powers  of  foresight.  The 
Latm  language  gives  great  scope  to  misconstructions, 
because  it  does  not  require  any  fixed  order  for  the  words 
of  a  sentence,  and  when  there  are  two  accusative  cases 
with  an  infinitive  verb,  it  may  be  difficult  to  tell  except 
from  the  context  which  comes  in  regard  to  sense  before 
the  verb.  The  double  me&uiug  which  may  be  given  to 
"  twice  two  and  three "  arises  from  amphibology ;  it 
may  be  7  or  10,  according  as  we  add  the  3  after  or  be- 
fore multiplying.  In  the  careless  construction  of  sen- 
tences it  is  often  impossible  to  tell  to  what  part  any 
adverb  or  qualifying  clause  refers.  Thus,  if  a  person 
says  '*I  accomplished  my  business  and  returned  the 
day  after,"  it  may  be  that  the  business  was  accomplished 
on  the  day  after  as  well  as  the  return;  but  it  may 
equally  have  been  finishsd  on  the  previous  day.  Any 
ambiguity  of  this  kind  may  generally  be  avoided  by  a 
simple  change  in  the  order  of  the  words ;  as  for 
instance,  "  I  accomplished  my  business,  and,  on  the  day 
after,  returned."  Amphibology  may  sometimes  arise 
from  confusing  the  subjects  and  predicates  in  a  com- 
pound sentence,  as  if  in  "platinum  and  iron  are  very 
rare  and  useful  metals,"  I  were  to  apply  the  predicate 
useful  to  platinum  and  rare  to  iron,  which  is  not 
intended.  The  word  "respectively"  is  often  used  to 
show  that  the  reader  is  not  at  liberty  to  apply  each 
predicate  to  each  subject. 

4.  The  Fallacy  of  Composition. 

The  Fallacy  of  Composition  is  a  special  case  ot  equivo- 
cation, arising  from  the  confusion  of  an  universal  and  a 


166  FALLACIES. 

collective  term.  In  the  premises  of  a  syllogism  we 
may  affirm  something  of  a  class  of  things  distributively^ 
that  is,  of  each  and  any  separately,  and  then  we  may  m 
the  conclusion  infer  the  same  of  the  whole  put  together. 
Thus  we  may  say  that  "  all  the  angles  of  a  triangle  are 
less  than  two  right  angles,"  meaning  that  any  of  the 
angles  is  less  than  two  right  angles  ;  but  we  must  not 
infer  that  all  the  angles  put  together  are  less  than  two 
right  angles.  We  must  not  argue  that  because  every 
member  of  a  jury  is  very  likely  to  judge  erroneously, 
the  jury  as  a  whole  are  also  very  hkely  to  judge  errone- 
ously ;  nor  that  because  each  of  the  witnesses  in  a  law 
case  is  liable  to  give  false  or  mistaken  evidence,  no  con- 
fidence can  be  reposed  in  the  concur'-ent  testimony  of  a 
number  of  witnesses. 

5.  The  Fallacy  of  Division. 

The  Fallacy  of  Division  is  the  converse  of  the  pre- 
ceding, and  consists  in  using  the  middle  term  collec- 
tively in  the  major  premise,  but  distributively  in  the 
minor,  so  that  the  whole  is  divided  into  its  parts.  Thus 
it  might  be  argued,  "  All  the  angles  of  a  triangle  are 
(together)  equal  to  two  right  angles  ;  -4  5 6' is  an  angle 
of  a  triangle;  therefore  ABC  is  equal  to  two  nght 
angles."  Or  again,  "The  inhabitants  of  the  town  con- 
sist of  men,  women  and  children  of  all  ages  ;  those 
who  met  in  the  Guildhall  were  inhabitants  of  the  town; 
therefore  they  consisted  of  men,  women  and  children 
of  all  ages;"  or,  "The  judges  of  the  court  of  appeal 
cannot  misinterpret  the  law ;  Lord  A.  B.  is  a  judge  of 
the  court  of  appeal ;  therefore  he  cannot  misinterpret 
the  law." 


LOGICAL   FALLACIES.  167 

6.  The  Fallacy  of  Accent. 

The  Fallacy  of  Accent  consists  in  any  ambiguity 
arising  from  a  misplaced  accent  or  emphasis  thrown 
upon  some  word  of  a  sentence.  A  ludicrous  instance  is 
liable  to  occur  in  reading  Chapter  XIII  of  the  First 
Book  of  Kings,  verse  27,  where  it  is  said  of  the  prophet 
*'And  he  spake  to  his  sons,  saying,  Saddle  me  the  ass. 
And  they  saddled  him.'''  The  italics  indicate  that  the 
word  him  was  supplied  by  the  translators  of  the  author- 
ized version,  but  it  may  suggest  a  very  different  mean- 
ing. The  Commandment  "  Thou  shalt  not  bear  false 
witness  against  thy  neighbor"  may  be  made  by  a 
slight  emphasis  of  the  voice  on  the  last  word  to  imply 
that  we  are  at  liberty  to  bear  false  witness  against  other 
persons.  Mr.  De  Morgan,  who  remarks  this,  also  points 
out  that  the  erroneous  quoting  of  an  author,  by  unfairly 
separating  a  word  from  its  context  or  italicising  words 
which  were  not  intended  to  be  italicised,  gives  rise  to 
cases  of  this  fallacy. 

It  is  curious  to  observe  how  many  and  various  may  be  the 
meanings  attributable  to  the  same  sentence  according  as 
emphasis  is  thrown  upon  one  word  or  another.  Thus  the  sen- 
tence "  The  study  of  Logic  is  not  supposed  to  communicate  a 
knowledge  of  many  useful  facts,"  may  be  made  to  imply  that  the 
study  of  Logic  does  communicate  such  a  knowledge,  although  it 
Is  not  supposed  to  ;  or  that  it  communicates  a  knowledge  of  &few 
useful  facts ;  or  that  it  communicates  a  knowledge  of  many  vse- 
less  facts.  This  ambiguity  may  be  explained  by  considering  that 
if  you  deny  a  thing  to  have  the  group  of  qualities  A,  B,  C,  D, 
the  truth  of  your  statement  will  be  satisfied  by  any  one  quality 
being  absent,  and  an  accented  pronunciation  will  often  be  used 
to  indicate  that  which  the  speaker  believes  to  be  absent.  If  you 
deny  that  a  particular  fruit  is  ripe  and  sweet  and  well-flavored 


168  t'ALLACt£S. 

it  may  be  unripe  and  sweet  and  well-flavored  ;  or  ripe  and  Bom 
and  well-flavored  ;  or  ripe  and  sweet  and  ill  flavored ;  or  uny  two 
or  even  all  three  qualities  may  be  absent.  But  if  you  deny  it  to 
be  ripe  and  sweet  and  well-flavored,  the  denial  would  be  under 
stood  to  refer  to  the  last  quality.  Jeremy  Bentham  was  so  much 
afraid  of  being  misled  by  this  fallacy  of  accent  that  he  employed 
a  person  to  read  to  him,  as  1  have  heard,  who  had  a  pwuliarly 
monotonous  manner  of  reading. 

7.  The  Fallacy  of  the  Figrnre  of  Speech. 

The  Fallacy  of  the  Figure  of  Speech  is  the  sixth  and 
last  of  the  semi-logical  fuUacies,  and  is  of  a  very  trifling 
character.  It  appears  to  consist  in  any  grammatical 
mistake  or  confusion  between  one  part  of  speech  and^ 
another.  Aristotle  gravely  gives  the  following  instance: 
"  Whatever  a  man  walks  he  tramples  on ;  a  man  walks 
the  whole  day  ;  therefore  he  tramples  on  the  day." 
Here  an  adverbial  phrase  is  converted  into  a  noun 
object. 

In  this  Section,  on  "  Log^ical  Fallacies,**  we  hav« 
considered  :— 

1 .  The  Classification  of  Logical  Fallacies, 

2.  The  Fallacy  of  Equivocation. 

3.  The  Fallacy  of  Amphibology, 

4.  The  Fallacg  of  Composition. 

5.  The  Fallacy  of  Division, 

6.  The  Fallacy  of  Accent, 

7.  The  Fallacy  of  the  Figure  of  Speech, 


MATERIAL  FALLACLB8.  169 

SECTION    II* 

MATERIAL    FALLACIES. 

1.  The  Classiiication  of  Material  Fallacies. 

The  Material  fallacies  are  next  to  be  considered  ;  and 
their  importance  is  very  great,  although  it  is  not  easy 
to  illustrate  them  by  brief  examples.  There  are  alto- 
gether seven  kinds  of  such  fallacies  enumerated  b> 
Aristotle  and  adopted  by  subsequent  logicians,  as  fol- 
lows : 

1.  The  Fallacy  of  Accident. 

2.  The  Converse  Fallacy  of  Accident. 

3.  The  Irrelevant  Conclusion. 

4.  The  Petitio  Principii. 

5.  The  Fallacy  of  the  Consequent  or  Non  sequitur 

6.  The  False  Cause. 

7.  The  Fallacy  of  Many  Questions. 

2.  The  Fallacy  of  Accident  and  its  Converse. 

Of  these  the  first  two  are  conveniently  described  to- 
gether. The  fallacy  of  accident  consists  in  arguing 
erroneously  fpom  a  general  rule  to  a  special  case,  where 
a  certain  accidental  circumstance  renders  the  rule  inap- 
phcable.  The  converse  fiillacy  consists  in  arguing  from 
a  special  case  to  a  general  one.  This  latter  fallacy  is 
usually  described  by  the  Latin  phrase  a  dicto  secundufn 
quid  ad  dictum  simpliciter,  meaning  "from  a  state- 
ment under  a  condition  to  a  statement  simply  or  with- 
9 


170  FALLACIES. 

out  that  condition."  Mr.  De  Morgan  has  remarked 
in  his  very  interesting  chapter  on  Fallacies*  that 
we  ought  to  add  a  third  fallacy,  which  would  con- 
sist in  arguing  from  one  special  case  to  another  speciax 
case. 

A  few  examples  will  illustrate  these  kinds  of  fallacy, 
but  much  difficulty  is  often  encountered  in  saying  to 
which  of  the  three  any  particular  example  is  best 
referred.  A  most  ancient  example  repeated  in  almost 
every  logical  hand-book  is  as  follows:  "What  you 
bought  yesterday  you  eat  to-day;  you  bought  raw  meat 
yesterday;  therefore  you  eat  raw  meat  to-day."  The 
assertion  in  the  conclusion  is  made  of  meat  with  the 
accidental  quality  of  rawness  added,  where  the  first 
premise  evidently  speaks  of  the  substance  of  the  meat 
without  regard  to  its  accidental  condition.  This  then 
is  a  case  of  the  direct  fallacy.  If  it  is  argued  again 
that  because  wine  acts  as  a  poison  when  used  in  ex- 
cess it  is  always  a  poison,  we  fall  into  the  converse 
fallacy. 

It  would  be  a  case  of  the  direct  fallacy  of  accident 
to  infer  that  a  magistrate  is  justified  in  using  his  power 
to  forward  his  own  religious  views,  because  every  man 
has  a  right  to  inculcate  his  own  opinions.  Evidently  a 
magistrate  as  a  man  has  the  rights  of  other  men,  but  in 
his  capacity  of  a  magistrate  he  is  distinguished  from 
other  men,  and  he  must  not  infer  of  his  special  powers 
in  this  respect  what  is  only  true  of  his  rights  as  a 
man.  For  another  instance  take  the  following:  "He 
who  thrusts  a  knife  into  another  person   should   be 

•  Formal  Logie,  Chap.  XJII. 


MATEBIAL  FALLACIES.  171 

punished;  a  surgeon  in  operating  does  so  ;  therefore  he 
should  be  punished."  Though  the  fallacy  of  this  is 
absurdly  manifest,  it  is  not  so  manifest  how  we  are  to 
classify  the  error.  We  may  for  instance  say  that  as  a 
general  rule  whoever  stabs  or  cuts  another  is  to  be 
punished  unless  it  can  be  shown  to  have  been  done 
under  exceptional  circumstances,  as  by  a  duly  qualified 
surgeon  acting  for  the  good  of  the  person.  In  this  case 
the  example  belongs  to  the  direct  fallacy  of  accident. 
In  another  view  we  might  interpret  the  first  premise  to 
mean  the  special  case  of  thrusting  a  knife  maliciously  ; 
to  argue  from  that  to  the  case  of  a  surgeon  would 
be  to  infer  from  one  special  case  to  another  special 
case. 

It  is  undoubtedly  true  that  to  give  to  beggars  pro- 
motes mendicancy  and  causes  evil ;  but  if  we  interpret 
this  to  mean  that  assistance  is  never  to  be  given  to 
those  who  solicit  it,  we  fall  into  the  converse  fallacy  of 
accident,  inferring  of  all  who  solicit  alms  what  is 
only  true  of  those  who  solicit  alms  as  a  profession. 
Similarly  it  is  a  very  good  rule  to  avoid  lawsuits 
and  quarrels,  but  only  as  a  general  rule,  since  there 
frequently  arise  circumstances  in  which  resort  to  the 
law  is  a  plain  duty.  Almost  all  the  diflBculties  which 
we  meet  in  matters  of  law  and  moral  duty  arise  from 
the  impossibility  of  always  ascertaining  exactly  to  what 
cases  a  legal  or  moral  rule  does  or  does  not  extend  ; 
hence  the  interminable  differences  of  opinion,  even 
among  the  judges  of  the  land. 

3.   The  Fallacy  of  Irrelevant  Conclusion. 

The  Third  Material  Fallacy  is  that  of  the  Irrelevant 


172  FALLACIES. 

Conclusion,  technically  called  the  Ignoratio  Elenchi,  or 
literally  Ignorance  of  the  Refutation.  It  consists  in 
arguing  to  the  wrong  point,  or  proving  one  thing  in 
such  a  manner  that  it  is  supposed  to  be  something  else 
that  is  proved.  Here  again  it  would  be  difficult  to 
adduce  concise  examples,  because  the  fallacy  usually 
occurs  in  the  course  of  long  harangues,  where  the 
multitude  of  words  and  figures  leaves  room  for  con- 
fusion of  thought  and  forgetful ness.  This  fallacy  is  in 
fact  the  great  resource  of  those  who  have  to  support  a 
weak  case.  It  is  not  unknown  in  the  legal  profes- 
sion, and  an  attorney  for  the  defendant  in  a  lawsuit 
is  said  to  have  handed  to  the  barrister  his  brief 
marked,  "No  case;  abuse  the  plaintiff's  attorney." 
Whoever  thus  uses  what  is  known  as  argumentum 
ad  hominem,  that  is  an  argument  which  rests,  not 
upon  the  merit  of  the  case,  but  the  character  or 
position  of  those  engaged  in  it,  commits  this  fallacy. 
If  a  man  is  accused  of  a  crime  it  is  no  answer  to 
say  that  the  prosecutor  is  as  bad.  If  a  great  change 
in  the  law  is  proposed  in  Parliament,  it  is  an  Irrele- 
vant Conclusion  to  argue  that  the  proposer  is  not 
the  right  man  to  bring  it  forward.  Every  one  who 
gives  advice  lays  himself  open  to  the  retort  that  he 
who  preaches  ought  to  practise,  or  that  those  who  live 
in  glass  houses  ought  not  to  throw  stones.  Never- 
theless there  is  no  necessary  connection  between  the 
character  of  the  person  giving  advice  and  the  goodness 
of  the  advice. . 

The  argumentum  ad  populum  is  another  form  of 
Irrelevant  Conclusion,  and  consists  in  addressing  argu- 
ments to  a  body  of  people  calculated  to  excite  their 


MATERIAL    FALLACIES.  173 

feeling  and  prevent  them  from  forming  a  dispassionate 
judgment  upon  the  matter  in  hand.  It  is  the  great 
weapon  of  rhetoricians  and  demagogues. 

4.  The  Fallacy  of  Petitio  Principil. 

Petitio  Principii  is  a  familiar  name,  and  the  nature  of 
the  fallacy  it  denotes  is  precisely  expressed,  in  the  phrase 
begging  the  question.  Another  apt  name  for  the  fallacy 
is  circulus  in  probando^  or  "a  circle  in  the  proof."  It 
consists  in  taking  the  conclusion  itself  as  one  of  the 
premises  of  an  argument.  Of  course  the  conclusion 
of  a  syllogism  must  always  be  contained  or  implied  in 
the  premiseSj  but  only  when  those  premises  are  com- 
bined, and  are  distinctly  different  assertions  from  the 
conclusion.    Thus  in  the  syllogism, 

5  is  C, 

A  is  5, 
therefore  A  is  G, 

the  conclusion  is  proved  by  being  deduced  from  two 
propositions,  neither  of  which  is  identical  with  it ;  but 
if  the  truth  of  one  of  these  premises  itself  depends 
upon  the  following  syllogism, 

C'V&By 

A\&  G, 
therefore  A  is  -B, 

it  is  plain  that  we  attempt  to  prove  a  proposition  by 
itself,  which  is  as  reasonable  as  attempting  to  support  a 
body  upon  itself.  It  is  not  easy  to  illustrate  this  kind 
of  fallacy  by  examples,  because  it   usually  occurs  in 


174  FALLACIES. 

long  aigiiiuetits,  and  especially  in  wordy  metaphysicdi 
writings.  We  are  very  likely  to  fall  into  it,  however, 
when  we  employ  a  mixture  of  Saxon  and  Latin  or 
Greek  words,  so  as  to  appear  to  prove  one  proposition 
by  another  which  is  really  the  same  expressed  in  differ 
ent  terms,  as  in  the  following:  "Consciousness  must 
be  immediate  cognition  of  an  object;  for  I  cannot  be 
said  really  to  know  a  thing  unless  my  mind  has  been 
affected  by  the  thing  itself.'* 

In  the  use  of  the  disjunctive  syllogism  this  fallacy  Is  likely  to 
happen  ;  for  by  enumerating  only  those  alternatives  which  favor 
one  view  and  forgetting  the  others  it  is  easy  to  prove  anything. 
An  instance  of  this  occurs  in  the  celebrated  sophism  by  which 
some  of  the  ancient  Greek  Philosophers  proved  that  motion  was 
impossible.  For,  said  they,  a  moving  body  must  move  either  in 
the  place  where  it  is  or  the  place  where  it  is  not ;  now  it  is  absurd 
that  a  body  can  be  where  it  is  not,  and  if  it  moves  it  cannot  be  in 
the  place  where  it  is;  therefore  it  cannot  move  at  all.  The 
error  arises  in  the  assumption  of  a  premise  which  begs  the  ques- 
tion ;  the  fact  of  course  is  that  the  body  moves  between  the  place 
where  it  is  at  one  moment  and  the  place  where  it  is  at  tlie  next 
moment. 

Jeremy  Bentham,  however,  pointed  out  that  the  use  even  of  a 
single  name  may  imply  a  Petitio  Principii.  Thus  in  a  Clmrch 
assembly  or  synod,  where  a  discussion  is  taking  place  as  to 
whether  a  certain  doctrine  should  be  condemned,  it  would  be  a 
Petitio  Principii  to  argue  that  the  doctrine  is  heresy,  and  there- 
fore it  ought  to  be  condemned.  To  assert  that  it  is  heresy  is  to 
beg  tlie  question,  because  every  one  understands  by  heresy  a 
di>ctrine  which  is  to  be  condemned.  Similarly  in  Parliament  a 
oill  is  often  opposed  on  the  ground  that  it  is  unconstitutional  and 
therefore  ought  to  be  rejected  ;  but  as  no  precise  definition  can  be 
given  of  what  is  or  is  not  constitutional,  it  means  little  more  than 
that  the  measure  in  distasteful  to  the  opponent.  Names  whlcL 
%re  used  in  this  fallacious  manner  were  aptly  called  by  Benthanu 


MATERIAL  FALLACIES.  176 

Question-begging  Epithets.     In  like  manner  we  beg  the  ques- 
♦ion  when  we  oppose  any  change  by  saying  that  it  is  uii-EnglUh. 

5.  The  Fallacy  of  the  Gousequent. 

The  Fallacy  of  the  Consequent  is  better  understood  by 
ihe  familiar  phrase  nou  sequitiir.  We  may  apply  this 
Jiame  to  any  argument  which  is  of  so  loose  and  incon- 
sequent a  character  that  no  one  can  discover  any 
cogency  in  it.  It  thus  amounts  to  little  more  than 
the  assertion  of  a  conclusion  which  has  no  connection 
with  the  premises.  Professor  De  Morgan  gives  as  an 
example  the  following:  "Episcopacy  is  of  Scripture 
origin ;  the  Church  of  England  is  the  only  Episcopal 
Church  in  England;  ergo,  the  Church  established  is 
the  Church  that  should  be  supported." 

O.  The  Fallacy  of  False  Cause. 

By  the  Fallacy  of  the  False  Cause  I  denote  that 
which  has  generally  been  referred  to  by  tlie  Latin 
phrase  non  causa  pro  causd.  In  this  fallacy  we  assume 
that  one  thing  is  the  cause  of  another  without  any 
sufficient  grounds.  A  change  in  the  weather  is  even 
yet  attributed  to  the  new  moon  or  full  moon  which  had 
occurred  shortly  before,  although  it  has  been  demon- 
strated over  and  over  again  that  the  moon  can  have 
no  such  effect.  In  former  centuries  any  plague  or  other 
public  calamity  which  followed  the  appearance  of  a 
comet  or  an  eclipse  was  considered  to  be  the  result 
of  it.  The  Latin  phrase  post  hoc  ergo  propter  hoe 
(after  this  and  therefore  in  consequence  of  tliis)  exactly 
describes  the  cliaracter  of  these  fallacious  conclusions. 


176  lALLAOIM. 

Though  we  no  longer  dread  signs  and  omens,  yec  wt 
often  enough  commit  the  fallacy ;  as  when  ^e  assume 
that  all  the  prosperity  of  England  is  the  result  of  the 
national  character,  forgetting  that  the  plentiful  coal  in 
the  country  and  its  maritime  position  have  contributed 
to  the  material  wealth.  It  is  no  doubt  equally  falla- 
cious to  attribute  no  importance  to  national  character, 
and  to  argue  that  because  England  has  in  past  centuries 
misgoverned  Ireland  all  the  present  evils  of  Ireland  are 
due  to  that  misgovemment 

7.  The  Fallacy  of  Many  Questions. 

Lastly,  there  is  the  somewhat  trivial  Fallacy  of  Many 
Questions,  which  is  committed  by  those  who  so  combine 
two  or  three  questions  into  one  that  no  true  answer  can 
be  given  to  them.  I  cannot  think  of  a  better  example 
than  the  vulgar  pleasantry  of  asking,  "  Have  you  left 
off  beating  your  mother  ?"  Questions  equally  as  unfair 
are  constantly  asked  by  barristers  examining  witnesses 
in  a  court  of  justice,  and  no  one  can  properly  be  re- 
quired to  answer  Yes  or  No  to  every  question  which 
may  be  addressed  to  him.  As  Aristotle  says,  ''Several 
questions  put  as  one  should  be  at  once  decomposed  into 
their  several  parts.  Only  a  single  question  admits  of  a 
single  answer:  so  that  neither  several  predicates  of  one 
subject,  nor  one  predicate  of  several  subjects,  but  only 
one  predicate  of  one  subject,  ought  to  be  affirmed  or 
ienied  in  a  single  answer." 

Bead  Professor  De  Morgan's  exw5ll<'nt  and  amusing  Cliaptei 

on  Fallacies,  Farmed  Logir,  Cl)ii|).  XIII. 
Whately's  Remarks  on  Fallacies,  Elements  of  Logic,  Book  III 

are  oftea  very  oriKinal  and  acut«. 


MATERIAL  FALLACIES.  177 

In   this    Section,  on  "Material  Fallacies,"  W€ 
have  considered : 

1.  The  Classiflcution  of  Material  F'allacies, 

2.  The  Fallacy  of  Accident  and  ittt  Cftnrerse, 

3.  The  Fallacy  of  Irrelevant  Conclusion* 

4.  The  Fallacy  of  Petitio  Principii, 
6.   The  Fallacy  of  the  Consequent. 

6.  T/ie  Fallacy  of  the  False  Cause, 

7.  TheFallacy  of  Many  Questions, 


SHAPTHB    ?. 

INDUCTION. 

The  subject  of  Induction,  as  u  process  of  inference, 
may  be  considered  under  the  following  divisions  :  (1) 
T/ie  Inductive  Syllogism ;  (2)  The  Forms 
of  Ifiduction, 


SEGTIOK    !♦ 

THE   INDUCTIVE   SYLLOGISM. 

1.  Induction  and  Deduction  Contra.sted. 

We  have  in  previous  chapters  considered  deductive 
reasoning,  which  consists  in  combining  two  or  more 
general  propositions  synthetically,  and  thus  arriving  at 
a  conclusion  which  is  a  proposition  or  truth  of  less 
generality  than  the  premises,  that  is  to  say,  it  applies  to 
fewer  individual  instances  than  the  separate  premises 
from  which  it  was  inferred.  When  I  combine  the 
general  truth  that  "  metals  are  good  conductors  of 
heat,"  with  the  truth  that  "aluminium  is  a  metal,"  1 
am  enabled  by  a  syllogism  in  the  mood  Barbara  to  infer 
that  "aluminium  is  a  good  conductor  of  heat."  As 
this  is  a  proposition  concerning  one  metal  only,  it  is 
evidently  less  general  than  the  premise,  which  referred 
to  all  metals  whatsoever.     In  induction,  on  the  con* 


INDUCTIOIf.  179 

trary,  we  proceed  from  less  general,  oi  even  from  indi- 
vidual facts,  to  more  general  propositions,  truths,  or,  as 
we  shall  often  call  them,  Laws  of  Nature.  When  it  is 
known  that  Mercury  moves  in  an  elliptic  orbit  round 
the  Sun,  as  also  Venus,  the  Earth,  Mars,  Jupiter,  etc., 
we  are  able  to  arrive  at  the  simple  and  general  truth 
that  "  all  the  planets  move  in  elliptic  orbits  round  the 
sun."  This  is  an  example  of  an  inductive  process  of 
reasoning. 

2,  Explanation  of  Traduction. 

It  is  true  that  we  may  reason  without  rendering  our 
conclusion  either  more  or  less  general  than  the  premises, 
as  in  the  following : 

Snowdon  is  the  highest  mountain  in  England  or  Wales ; 
Snowdon  is  not  so  high  as  Ben  Nevis ; 
Therefore  the  highest  mountain  in  England  or  Wales  is 
not  so  high  as  Ben  Nevis. 

Again ; 

Lithium  is  the  lightest  metal  known  ; 

Lithium  is  the  metal  indicated  by  one  bright  red  line 
in  the  spectrum; 

Therefore  the  lightest  metal  known  is  the  metal  indi- 
cated by  a  spectrum  of  one  bright  red  line. 

In  these  examples  all  the  propositions  are  singular 
propositions,  and  merely  assert  the  identity  of  singular 
terms,  so  that  there  is  no  alteration  of  generality.  Each 
conclusion  applies  to  just  such  an  object  as  each  of  the 
premises  applies  to.  To  this  kind  of  reasoning  the  apt 
name  of  Traduction  has  been  given. 


180  INDUCTION. 

3.  Importance  of  Induction. 

Induction  is  a  much  more  difficult  and  more  impor- 
tant kind  of  reasoning  process  than  Traduction  or  even 
Deduction  ;  for  it  is  engaged  in  detecting  the  general 
laws  or  uniformities,  the  relations  of  cause  and  effect, 
or  in  short  all  the  general  truths  that  may  be  asserted 
concerning  the  numberless  and  very  diverse  events  that 
take  place  in  the  natural  world  around  us.  The  greater 
part,  and  some  philosophers  think  the  wliole,  of  our 
knowledge,  is  ultimately  due  to  inductive  reasoning. 
The  mind,  it  is  plausibly  said,  is  not  furnished  with 
knowledge  in  the  form  of  general  propositions  ready 
made  and  stamped  upon  it,  but  is  endowed  with  powers 
of  observation,  comparison,  and  reasoning,  which  are 
adequate,  when  well  educated  and  exercised,  to  procure 
knowledge  of  the  world  without  us  and  the  world  within 
the  human  mind.  Even  when  we  argue  synthetically 
and  deductively  from  simi)le  ideas  and  truths  which 
seem  to  be  read}-  in  the  mind,  as  in  the  case  of  the 
science  of  geometry,  it  may  be  that  we  have  gathered 
those  simple  ideas  and  truths  from  previous  observation 
or  induction  of  an  almost  unconscious  kind.  This  is  a 
debated  point  upon  which  I  will  not  here  speak  posi- 
tively ;  but  if  the  truth  be  as  stated.  Induction  will  b(- 
the  mode  by  which  all  the  materials  of  knowledge  are 
brought  to  the  mind  and  analyzed.  Deduction  will 
then  be  the  almost  equally  important  process  by  which 
the  knowledge  thus  acquired  is  utilized,  and  by  which 
new  inductions  of  a  more  complicated  character,  as  we 
shall  see,  are  rendered  possible. 


INDUCTIVE   SYLLOQISMS.  18i 

4.  Perfect  and  Imperfect  Induction. 

An  luductioii,  that  is  an  act  of  Inductive  reasoning, 
m  called  Perfect  wheu  all  the  possible  cases  or  instances 
to  which  the  conclusion  can  refer,  have  been  examined 
and  enumerated  in  the  premises.  K,  as  usually  happens, 
it  is  impossible  to  examine  all  cases,  since  they  may 
occur  at  future  times  or  in  distant  parts  of  the  earth  or 
other  regions  of  the  universe,  the  Induction  is  called 
Imperfect.  The  assertion  that  all  the  months  of  the 
year  are  of  less  length  than  thirty-two  days  is  derived 
from  Perfect  Induction,  and  is  a  certain  conclusion 
because  the  calendar  is  a  human  institution,  so  that  we 
know  beyond  doubt  how  many  months  there  are,  and 
can  readily  ascertain  that  each  of  them  is  less  than 
thirty'two  days  in  length.  But  the  assertion  that  all 
the  planets  move  in  one  direction  round  the  sun,  from 
"West  to  East,  is  derived  from  Imperfect  Induction;  for 
it  is  possible  that  there  exist  planets  more  distant  than 
the  most  distant-known  planet  Neptune,  and  to  such  ft 
planet  of  course  the  assertion  would  apply. 

'J.   The  Difference  between  Perfect  and  Imper- 
fect Induction. 

It  is  obvious  that  there  is  a  great  difference  between 
Perfect  and  Imperfect  Induction.  The  latter  includes 
some  process  by  which  we  are  enabled  to  make  asser- 
tions concerning  things  that  we  have  never  seen  or 
examined  or  even  known  to  exist.  But  it  must  be  care- 
fully remembered  also  that  no  Imperfect  Induction  can 
give  a  certain  conclusion.  It  may  be  highly  probable 
or  nearly  certain  that  the  cases  unexamined  will  re- 


188  INDUCTION. 

semble  those  which  have  been  examined,  but  it  can 
never  be  certain.  It  is  quite  possible,  for  instance, 
that  a  new  planet  might  go  round  the  sue  in  an  opposite 
direction  to  the  other  planets.  In  the  case  of  the  satel- 
lites belonging  to  the  planets  more  than  one  exception 
of  this  kind  has  been  discovered,  and  mistakes  have 
constantly  occurred  in  science  from  expecting  that  all 
new  cases  would  exactly  resemble  old  ones.  Imperfect 
Induction  thus  gives  only  a  certain  degree  of  proba- 
bility or  likelihood  that  all  instances  will  agree  with 
those  examined.  Perfect  Induction,  on  the  other  hand, 
gives  a  necessary  and  certain  conclusion,  but  it  asserts 
nothing  beyond  what  was  asserted  in  the  premises. 

Mr.  Mill,  indeed,  differs  from  almost  all  other  logicians  in  hold- 
ing that  Perfect  Induction  is  improperly  called  Induction,  because 
it  does  not  lead  to  any  new  knowledge.  He  defines  Induction  as 
inference  from  the  known  to  the  unknotcn,  and  considers  the  unex- 
amined cases  which  are  apparently  brought  into  our  knowledge 
as  the  only  gain  from  the  process  of  reasoning.  Hence  Perfect 
Induction  seems  to  him  to  be  of  no  scientific  value  whatever,  be- 
cause the  conclusion  is  a  mere  reassertion  in  a  briefer  form,  a 
mere  summing  up  of  tne  premises.  I  may  point  out,  however, 
that  if  Perfect  Induction  were  no  more  than  a  process  of  abbre 
viation  it  is  yet  of  great  importance,  and  requires  to  be  continu- 
ally used  in  science  and  common  lite.  Without  it  we  could  never 
make  a  comprehensive  btatement,  but  should  be  obliged  to  enu- 
merate every  particular.  After  examining  the  books  in  a  library 
and  finding  them  to  be  all  English  lK)oks  we  .should  be  unable 
to  sum  up  our  results  in  the  one  projiosition,  "all  the  books  in 
this  library  are  English  books;"  but  should  be  required  to  go 
over  the  list  of  books  every  time  we  desired  to  make  any  one 
acquainted  with  the  contents  of  the  library.  The  fact  is,  that 
the  power  of  expressing  a  great  number  of  particular  facts  in  a 
very  brief  space  is  essential  to  the  progress  of  science.  Just  as 
the  whole  science  of  arithmetic  consistv  in  nothing  but  a  series  of 


INDUCTIVE  SYLLOGISM.  188 

processes  for  abbreviating  addition  and  subtraction,  and  enabling 
us  to  deal  with  a  great  number  of  units  in  a  very  short  time,  so 
Perfect  Induction  is  absolutely  necessary  to  enable  us  to  deal 
with  a  great  number  of  particular  facts  in  a  very  brief  space. 

6.  The  Perfect  Inductive  Syllogism. 

It  is  iisuul  to  represent  Perfect  Induction  in  the 
form  of  an  Inductive  Syllogism,  as  in  the  following 
instance . — 

Mercury,  Venus,  the  Earth,  etc.,  all  move  round  the 

sun  from  West  to  East; 
Mercury,  Venus,  the  Earth,  etc.,  are  all  the  known 

Planets ; 
Therefore  all  the  known  planets  move  round  the  sun 

from  West  to  East. 

This  argument  is  a  true  Perfect  Induction  because 
the  conclusion  only  makes  an  assertion  of  all  knoioi 
planets,  which  excludes  all  reference  to  possible  future 
discoveries  ;  and  we  may  suppose  that  all  the  known 
planets  have  been  enumerated  in  tiie  premises.  The 
form  of  the  argrmient  appears  to  be  tliat  of  a  syllogism 
in  the  third  figure,  namely  Darapti,  the  middle  term 
consisting  in  the  group  of  the  known  planets.  In 
reality,  however,  it  is  not  an  ordinary  syllogism.  The 
minor  premise  states  not  that  Mercury,  Venus,  the 
Earth,  Neptunt,  etc.,  are  contained  among  the  known 
planets,  but  that  they  are  those  planets,  or  are  identi- 
cal with  them.  This  premise  is  then  a  doubly  uni- 
versal proposition  of  a  kind  not  recognized  in  the  Aris- 
totelian Syllogism.  Accordingly  we  may  observe  thai 
the  conclusion  is  a  universal  proposition,  which  is  not 
allowable  in  the  third  figure  of  the  syllogism. 


184  INDUCTION. 

As  another  example  of  a  Perfect  Induction  we  maj 
take — 
January,  February December,  each  contain  lesa 

than  32  days. 

January December  are  all  the  months  of  the  year. 

Therefore  all  the  months  of  the  year  contain  less  than 

32  days. 

7.  The  Perfect  Inductive  Syllogism  Di^unctlve, 

Although  Sir  W.  Hamilton  has  entirely  rejected  the 
notion,  it  seems  worthy  of  inquiry  whether  the  Induc- 
tive Syllogism  be  not  really  of  the  Disjunctive  form  of 
/Syllogism.  Thus  I  should  be  inclined  to  represent  the 
last  example  in  the  form : 

A  month  of  the  year  is  either  January,  or  February, 

or  March or  December ;  but  January  has  less 

than  32  days ;  and  February  has  less  than  32  days ;  and 
80  on  until  we  come  to  December,  which  has  less  than 
32  days. 

It  follows  clearly  that  a  month  must  in  any  case  have 
less  than  32  days  ;  for  there  are  only  12  possible  cases, 
and  in  each  case  this  is  affirmed.  The  fact  is  that  the 
major  premise  of  the  syllogism  given  above  is  a  com- 
pound sentence  with  twelve  subjects,  and  is  there- 
fore equivalent  to  twelve  distinct  logical  propositions. 
The  minor  premise  is  either  a  disjunctive  proposition, 
as  I  have  represented  it,  or  something  quite  different 
from  anything  we  have  elsewhere  had. 

8.  The  Imperfect  Inductive  Syllogrism. 

From  Perfect  Induction  we  shall  have  to  pass  to 
Imperfect  Induction  ;  but  the  opinions  of  Logicians  are 


INDUCTIVE    SYLLOGISM.  186 

not  in  agreement  as  to  the  grounds  upon  which  we  are 
warranted  in  taking  a  part  of  the  instances  only,  and 
concluding  that  what  is  true  of  those  is  true  of  all. 
Thus  if  we  adopt  the  example  found  in  many  books  and 
say— 

This,  that,  and  the  other  magnet  attract  iron  ; 
This,  that,  and  the  other  magnet  are  all  magnets ; 
Therefore  all  magnets  attract  iron, 

»ve  evidently  employ  a  false  minor  premise,  because  this, 
that,  and  the  other  magnet  which  we  have  examined, 
cannot  possibly  be  all  existing  magnets.  In  whatever 
form  we  put  it  there  must  be  an  assumption  that  the 
magnets  which  we  have  examined  are  a  fair  specimen 
of  all  magnets,  so  that  what  we  find  in  some  we  may 
expect  in  all.  Archbishop  Whately  considers  that  this 
assumption  should  be  expressed  in  one  of  the  premises, 
and  he  represents  Induction  as  a  Syllogism  in  Barbara 
\a  follows : 

That  which  belongs  to  this,  that,  and  the  other  magnet, 

belongs  to  all ; 
Attracting  iron  belongs  to  this,  that,  and  the  other; 
Therefore  it  belongs  to  all. 

9.  The  Fundamental  Assumption  of  Induction. 

But  though  the  above  is  doubtless  a  correct  expres- 
sion of  the  assumption  made  in  an  Imperfect  Induc- 
tion, it  does  not  in  the  least  explain  the  grounds  on 
which  we  are  allowed  to  make  the  assumption,  and 
under  what  circumstances  such  an  assumption  would 
be  likely  to  prove  true.  Some  writers  have  asserted 
that  there  is  a  Principle,  called  the  Uniformity  of  Nature, 


186  INDUCTION. 

which  enables  us  to  afl&rm  that  what  has  often  been 
found  to  be  true  of  anything  will  continue  to  be  found 
true  of  the  same  sort  of  thing. 

In  his  original  work,  and  also  in  liis  "  Principles  of  Science,* 
Professor  Jevons  expresses  liis  dissent  from  the  doctrine  of  tho 
Uniformity  of  Nature.  This  has  led  him  into  a  controversy  which 
it  would  be  only  perplexing  to  review  in  tliis  connection,  and  the 
student  is  therefore  referred  below  to  the  authorities  who  have 
most  ably  treated  the  subject.  It  is  perhaps  sufficient  for  the 
young  learner  to  know  that  the  truth  of  the  doctrine  of  the 
Uniformity  of  Nature  is  essential  to  the  validity  of  an  Imperfect 
Induction. 

The  advanced  student  may  consult  the  following  with  advan- 
tage: 
Hansel's  Aldrich,  Appendix,  Notes  Q  and  H. 
Hamilton's  Lectures  on  Logic,  Lecture  XVII,  and  Appendix 

VII,  On  Induction  and  Exumple. 
J.  3.  Mill's  System  of  Logic,  Book  III,  Chap.  2,  Of  Inductions 

im^operly  HO-ealled.      Also,  Jevons'  Principles  of  Science, 

pp.  218,  229 ;  and  Fowler's  Inductive  Logic,  Third  Edition, 

pp.  xi,  xxiii. 

In  this  section,  on  "The  Inductive  Syllogrism,*' 
we  have  considered  : — 

1.  Induction  and  Deduction  Contrasted. 

2.  The  Explanation  of  Traduction. 

3.  The  Importance  of  Induction. 

4.  Perfect  and  Imperfect  Induction. 

5.  The  Difference  between  Perfect  and  Imperfed 
Induction. 

6.  Tlie  Perfect  luductire  Sf/lloffism. 

7.  The  Perfect  Inductive  Sf/l/of/isiu  Disjunctive. 

8.  The  Imperfect  Inductive  Sifllogism. 

9.  Tlie  FundamenUU  Assumption  of  Induction, 


FOBMS  OF  INDUCTION.  187 


8BCTIGH    11. 

THE  FORMS   OF  INDUCTION. 
1.  The  Character  of  the  Data. 

It  is  now  indispensable  that  we  should  consider  with 
great  care  upon  what  grounds  Imperfect  Induction  is 
founded.  No  difficulty  is  encountered  in  Perfect  In- 
duction because  all  possible  cases  which  can  come 
under  the  general  conclusion  are  enumerated  in  the 
premises,  so  that  in  fact  there  is  no  information  in  the 
conclusion  which  was  not  given  in  the  premises.  In 
this  respect  the  Inductive  Syllogism  perfectly  agrees 
with  the  general  principles  of  deductive  reasoning, 
which  require  that  the  information  contained  in  the 
conclusion  should  be  shown  only  from  the  data,  and 
that  we  should  merely  unfold,  or  transform  into  an 
explicit  statement  what  is  contained  in  the  premises 
implicitly. 

In  Imperfect  Induction  the  process  seems  to  be  of  a 
«ieholly  different  chr.raeter,  since  the  instances  concern- 
ing which  we  acquire  knowledge  may  be  infinitely  more 
numerous  than  those  from  which  we  acquire  the  knowl- 
edge. 

(1)  Geometrical  Reasoning  has  a  close  resemblance 
to  inductive  reasoning.  When  in  the  fifth  proposition 
of  the  first  book  of  Euclid  we  prove  that  tlie  angles  at 
the  base  of  an  isosceles  triangle  are  equal  to  each  other, 
it  is  done  by  taking  one  particular  triangle  as  an  ex- 
ample.   A  figure  i^  given  which  the  reader  is  requested 


188  INDUCTION. 

to  regard  as  having  two  equal  sides,  and  it  is  conclu. 
Bively  proved  that  if  the  sides  be  really  equal  then  the 
angles  opposite  to  those  sides  must  be  equal  also.  But 
Euclid  says  nothing  about  other  isosceles  triangles  ;  he 
treats  one  single  triangle  as  a  sufficient  specimen  of  all 
isosceles  triangles,  and  we  are  asked  to  believe  that 
what  is  true  of  that  is  true  of  any  other,  whether  its 
Sides  be  so  small  as  to  be  only  visible  in  a  microscope, 
or  so  large  as  to  reach  to  the  furthest  fixed  star.  There 
may  evidently  be  an  infinite  number  of  isosceles  tri- 
angles as  regards  the  length  of  the  equal  sides,  and  each 
of  these  may  be  infinitely  varied  by  increasing  or 
diminishing  the  contained  angle,  so  that  the  number  of 
possible  isosceles  triangles  is  infinite ;  and  yet  we  are 
asked  to  believe  of  this  incomprehensible  number  of 
objects  what  we  have  proved  only  of  one  single  speci- 
men. This  might  seem  to  be  the  most  extremely  Im- 
perfect Induction  possible,  and  yet  every  one  allows 
that  it  gives  us  really  certain  knowledge.  We  do  know 
with  as  much  certainty  as  knowledge  can  possess,  that 
if  lines  be  conceived  as  drawn  from  the  earth  to  two 
stars  equally  distant,  they  will  make  equal  angles  with 
the  line  joining  those  stars  ;  and  yet  we  can  never  have 
tried  the  experiment. 

The  generality  of  this  geometrical  reasoning  evidently 
depends  upon  the  certainty  with  which  we  jcnow  that 
all  isosceles  triangles  exactly  resemble  each  other.  The 
proposition  proved  does  not  in  fact  apply  to  a  triangle 
unless  it  agrees  with  our  specimen  in  all  the  qualities 
essential  to  the  proof.  The  absolute  length  of  any  of 
the  sides  or  the  absolute  magnitude  of  the  angle  con- 
tained between  any  of  them  were  not  points  upon  which 


FOEMS  OF  INDUCTION.  189 

the  proof  depended — they  were  purely  accidentel  cir- 
cumstances; hence  we  are  at  perfect  liberty  to  apply  to 
all  new  cases  of  an  isosceles  triangle  what  we  learn  of 
one  case. 

Upon  a  similar  ground  rests  all  the  vast  body  of  certain  knowl- 
edge  contained  in  the  mathematical  sciences — not  only  all  the 
geometrical  truths,  but  all  general  algebraical  truths.  It  was 
shown,  for  instance,  in  page  61,  that  if  a  and  6  be  two  quantities, 
and  we  multiply  together  their  sum  and  difference,  we  get  the 
difference  of  the  squares  of  a  and  h.  However  often  we  try  this 
it  will  be  found  true;  thus  if  a=10  and  6=7,  the  product  of  the 
sum  and  difference  is  17x3=51;  the  squares  of  the  quantities 
are  10  x  10  or  100  and  7  x  7  or  49,  the  difference  of  which  is  also 
61.  But  however  often  we  tried  the  rule,  no  certainty  would  be 
added  to  it:  because  when  proved  algebiaically  there  was  no 
condition  which  restricted  the  result  to  any  particular  numbers, 
and  a  and  6  might  consequently  be  any  numbers  whatever.  This 
generality  of  algebraical  reasoning  by  which  a  property  is  proved 
of  infinite  varieties  of  numbers  at  once,  is  one  of  the  chief  ad- 
vantages of  algebra  over  arithmetic. 

(2)  Mathematical  Induction,  or  Demonstrative  Induc- 
tion, is  a  process  wliich  shows  the  powers  of  reasoning 
in  a  very  conspicuous  way.  A  good  example  is  found  in 
the  following  problem : — If  we  take  the  first  hco  con- 
secutive odd  numbers,  1  and  3,  and  add  them  together, 
the  sum  is  4,  or  exactly  ticice  two ;  if  we  take  three 
such  numbers  1+3  +  5,  the  sum  is  9,  or  exactly  three 
times  three;  if  we  take /o'/r,  namely  l+3-r5+7,  the 
sura  is  16,  or  exactly  /o!/r  times  four  ;  or  generally,  if  we 
take  any  given  number  of  the  series,  1  +  3  +  5  +  7+-  .. 
the  sum  is  equal  to  the  number  of  the  terms  multiplied 
by  itself.  Any  one  who  knows  a  very  little  algebra  can 
prove  that  this  remarkable  law  is  universally  true,  oa 


190  INDUCTION. 

follows  :  Let  n  be  the  number  of  terms,  and  assume  for 
a  moment  that  this  law  is  true  up  to  n  terms,  thus — 

1+3  +  5  +  7+    ...+(2w— 1)  =  ««. 

Now  add  2n  + 1  to  each  side  of  the  equation.  It  fol 
lows  that — 

1  +  3  f  5  +  7+ +(2w— l)  +  (3«  +  l)  =  ;i2  +  3«_f-i. 

But  the  last  quantity  w^  +  ^w  +  l  is  just  equal  to 
(m  +  1)2;  so  that  if  the  law  is  true  for  n  terms  it  is  true 
also  for  w  +  1  terms.  We  are  enabled  to  argue  from 
each  single  case  of  the  law  to  the  next  case ;  but  we 
have  already  shown  that  it  is  true  of  the  first  few  cases, 
therefore  it  must  be  true  of  all.  By  no  conceivable 
Jabor  could  a  person  ascertain  by  trial  what  is  the  sum 
of  the  first  billion  odd  numbers,  and  yet  symbolically 
or  by  general  reasoning  we  know"  with  certainty  that 
they  would  amount  to  a  billion  billion,  and  neither 
more  nor  less  even  by  a  unit.  This  process  of  Mathe- 
matical Induction  is  not  exactly  the  same  as  Geo- 
metrical Induction,  because  each  case  depends  upon  the 
last,  but  the  proof  rests  upon  an  equally  narrow  basis 
of  experience,  and  creates  knowledge  of  equal  certainty 
and  generality.  Such  mathematical  truths  depend 
upon  observation  of  a  few  cases,  but  they  acquire  cer 
tainty  from  the  perception  we  have  of  the  exact  similarity 
of  one  case  to  another,  so  that  we  undoubtingly  believe 
what  is  true  of  one  case  to  bo  true  of  another. 

(3)  Uncertain  Data. — It  is  very  instructive  to  contrast 
with  these  cases  certain  other  ones  where  there  is  a  like 
ground  of  observation,  but  not  the  same  tie  of  similarity. 
It  was  at  one  time  believed  that  if  any  integral  number 
were  multiplied  by  itself,  added  to  itself  and  then  added 


FORMS  OF   INDUCTION.  191 

to  41,  the  result  would  be  a  prime  number,  that  is  a 
number  which  could  not  be  divided  by  any  other  in* 
tegral  number  except  unity ;  in  symbols, 

a:*+a:  +  4:l=prime  number. 

This  was  believed  solely  on  the  ground  of  trial  and 
experience,  and  it  certainly  holds  for  a  great  many 
values  of  x.  Thus,  when  x  is  successively  made  equal 
to  the  numbers  in  the  first  line  below,  the  expression 
a^+a:-}-41  gives  the  values  in  the  second  line,  and  they 
are  all  prime  numbers: 

0123456789       10 
41     43     47     53     61     71     83     97     113   131    151 

No  reason,  however,  could  be  given  why  it  should 
always  be  true,  and  accordingly  it  is  found  that  the 
rule  does  not  always  hold  true,  but  fails  when  a;^40. 
Then  we  have  40  x  40  +  40  +  41  =  1681,  but  this  is  clearly 
equal  to  41x40  +  41  or  41x41,  and  is  not  a  prime 
number. 

In  that  branch  of  mathematics  which  treats  of  the  peculiar 
properties  and  kinds  of  numbers,  other  propositions  depending 
solely  upon  observation  have  been  asserted  to  be  always  true. 

Thus  Fermat  believed  that  2^  +  1  always  represents  a  prime 
number,  but  could  not  give  any  reason  for  the  assertion.  It 
holds  true  in  fact  until  the  product  reaches  the  large  number 
4294967297,  which  was  found  to  be  divisible  by  641,  so  that  the 
generality  of  the  statement  was  disproved. 

We  find  then  that  in  some  cases  a  single  Instance 
proves  a  general  and  certain  rule,  while  in  others  a  very 
great  number  of  instances  are  insufficient  to  give  any 
certainty  at  all;  all  depends  upon  the  perception    we 


192  DTDUOTION. 

have  of  similarity  or  identity  between  one  casb  and  an- 
other. We  can  perceive  no  similarity  between  all  prime 
numbers  which  assures  us  that  because  one  is  repre- 
sented by  a  certain  formula,  also  another  is ;  but  we 
do  find  such  similarity  between  the  sums  of  odd  num- 
bers, or  between  isosceles  triangles. 

(4)  Inductions  in  Physical  Science  Involve  Exactly 
Similar  Differences. — When  a  chemist  analyzes  a  few 
grains  of  water  and  finds  that  they  contain  exactly  8 
parts  of  oxygen  and  1  of  hydrogen  for  9  parts  of  water, 
he  feels  warranted  in  asserting  that  the  same  is  true  of 
all  pure  water  whatever  be  its  origin,  and  whatever  be 
the  part  of  the  world  from  which  it  conies.  But  if  he 
analyze  a  piece  of  granite,  or  a  sample  of  sea-water  from 
one  part  of  the  world,  he  does  not  feel  any  confidence 
that  it  will  resemble  exactly  a  piece  of  granite,  or  a 
sample  of  sea-water  from  another  part  of  the  earth ; 
hence  he  does  not  venture  to  assert  of  all  granite  or 
sea-water,  what  he  finds  true  of  a  single  sample.  Ex- 
tended experience  shows  that  granite  is  very  variable  in 
composition,  but  that  sea-water  is  rendered  pretty  uni- 
form by  constant  mixture  of  currents.  Nothing  but 
experience  in  these  cases  could  inform  us  how  far  we 
may  assert  safely  of  one  sample  what  we  have  ascertained 
of  anc^ther.  But  we  have  rejison  to  believe  that  chemi- 
cal compounds  are  naturally  fixed  and  invariable  in 
composition,  according  to  Dalton's  laws  of  combining 
proportions.  No  d  priori  reasoning  from  the  principles 
of  thought  could  have  told  us  this,  and  we  only  learn 
it  by  extended  experiment.  But  having  once  shown  it 
to  be  true  with  certain  substances  we  do  not  need  to 
repeat  the  trial  with  all  other  substances,  because  W4 


FORMS  OF   INDUCTION.  198 

have  every  reason  to  believe  that  it  is  a  natural  law  in 
which  all  chemical  substances  resemble  each  other.  It 
is  only  necessary  then  for  a  single  accurate  analysis  of  a 
given  fixed  compound  to  be  made  in  order  to  inform 
us  of  the  composition  of  all  other  portions  of  the  same 
substance. 

It  must  be  carefully  observed,  however,  that  all  in- 
ductions in  physical  science  are  only  probable,  or  that 
if  certain,  it  is  only  liypotheticul  certainty  they  possess. 
Can  I  be  absolutely  i)ertain  that  all  water  contains  one 
part  of  hydrogen  in  nine  ? "  I  am  certain  only  on  two 
conditions : — 

1.  That  this  was  certainly  the  composition  of  the 
sample  tried. 

2.  That  any  other  substance  I  call   water  exactly 

resembles  that  sample. 
But  even  if  the  first  condition  be  undoubtedly  true,  I 
tan  not  be  certain  of  the  second.  For  how  do  I  know 
what  is  water  except  by  the  fact  of  its  being  a  trans- 
parent liquid,  freezing  into  a  solid  and  evaporating  into 
steam,  possessing  a  high  specific  heat,  and  a  number  of 
other  distinct  properties?  But  can  I  be  absolutely  cer- 
tain that  every  liquid  possessing  all  these  properties  is 
water?  Practically  I  can  be  certain,  but  theoretically 
I  cannot.  Two  substances  may  have  been  created  so 
like  each  other  that  we  should  never  yet  have  discovered 
the  diflference  ;  we  might  then  be  constantly  misled  by 
assuming  of  the  one  what  is  only  true  of  the  other. 
That  this  should  ever  happen  with  substances  possess- 
ing the  very  distinct  qualities  of  water  is  excessively 
improbable,  but  so  far  is  it  from  being  impossible  oi 
improbable  in  other  cases,  that  it  has  often  happened. 
9 


194  INDUCTION. 

Most  of  the  new  elements  discovered  in  late  years  havo,  with 
out  doubt,  been  mistaken  proviously  for  other  elements.  Caesium 
and  Rubidium  hud  bi;en  long  mistaken  for  each  other,  and  lor 
Potassium,  before  they  were  distinguished  by  Bunsen  and  Kirch- 
hoff  by  means  of  the  spectroscope.  As  they  are  now  known  to 
be  widely  distributed,  although  in  small  quantities,  it  is  certain 
that  what  was  supposed  to  be  Potassium  in  many  thousands  of 
analyses  was  partly  composed  of  different  substances.  Selenium 
had  probably  been  confused  with  Sulphur,  and  there  are  certain 
metals — for  instance,  Rhodium,  Ruthenium,  Iridium,  Osmium, 
and  Beryllium — Yttrium,  Erbium,  Cerium,  Lanthanum,  and 
Didymium — Cadmium  and  Indium— which  have  only  recently 
been  distinguished.  The  progress  of  science  will  doubtless  show 
that  we  are  mistaken  in  many  of  our  identifications,  and  various 
difficulties  thus  arising  will  ultimately  be  explained. 

(5)  Future  Phenomena. — Take  again  a  very  ditferent 
case  of  induction.  Are  we  certain  that  the  sun  will  rise 
again  to-morrow  morning  as  it  has  risen  for  many 
thousand  years,  and  probably  for  some  hundred  million 
years?  We  are  certain  only  on  this  condition  or  hypo- 
thesis, that  the  planetary  system  proceeds  to-morrow  as 
it  has  proceeded  for  so  long.  Many  causes  m>iy  exist 
which  might  at  any  moment  defeat  all  our  calculations  ; 
our  sun  is  believed  to  be  a  variable  star,  and  foi  what 
we  know  it  might  at  any  moment  suddenly  explode  or 
flare  up,  as  certain  other  stars  have  been  observec*  to 
do,  and  we  should  then  be  all  turned  into  thin  lumi- 
nous vapor  in  a  moment  of  time.  It  is  not  at  ail  impos- 
sible that  a  collision  did  once  occur  in  the  planetary 
system,  and  that  the  minute  planets  or  asteroids  are  the 
result.  Even  if  there  is  no  large  meteor,  comet  or 
other  body  capable  of  breaking  up  the  earth  bv  colli- 
sion, yet  it  is  probable  that  the  sun  moves  throng-^  space 
at  the  rate  of  nearly  300  miles  per  minute,  and  J*  •^^me 


FORMS   OF    INDUCTION.  195 

other  star  should  meet  us  at  a  similar  rate  the 
consequences  would  be  inconceivably  terrible.  It 
is  highly  improbable,  however,  that  such  an  event 
should  come  to  pass  even  in  the  course  of  a  million 
years. 

(G)  General  Law  from  the  Inspection  of  Data. — No 
mere  Imperfect  Induction  can  give  certain  knowledge ; 
all  inference  proceeds  upon  the  assumption  that  new 
instances  will  exactly  resemble  old  ones  in  all  material 
circumstances;  but  in  natural  phenomena  this  is  purely 
hypothetical,  and  we  may  constantly  find  ourselves  in 
error.  In  Mathematical  Induction  certainty  arose  from 
the  cases  being  hypothetical  in  their  own  nature,  or 
being  made  so  as  exactly  to  correspond  with  the  condi- 
tions. We  cannot  assert  that  any  triangle  existing  in 
nature  has  two  equal  sides  or  two  equal  angles,  and  it 
is  even  impossible  in  practice  that  any  two  lines  or 
angles  can  be  absolutely  equal.  But  it  is  nevertheless 
true  that  if  the  sides  are  equal  the  angles  are  equal. 
All  certainty  of  inference  is  thus  relative  and  hypothe- 
■  tical.  Even  in  the  syllogism  the  certainty  of  the  con- 
clusion only  rests  on  the  hypothesis  of  certainty  in 
the  premises.  It  is  probable,  in  fact,  that  all  reason- 
ing reduces  itself  to  a  single  type — that  what  is  true  of 
one  thing  will  be  true  of  another  thing,  on  condition  of 
there  being  an  exact  resemblance  between  them  in  all 
material  circumstances. 

2.  Special  Kinds  of  Induction. 

There  are   two   special  varieties  of  Induction  that 
deserve  to  be  more  particularly  noticed : 

(1)  Reasoning  by  Analogy. — In  strictness  an  analogy 


196  INDUCTION. 

is  not  an  identity  of  one  thing  with  another,  but  an 
identity  of  relations.  In  the  case  of  numbers  7  is  not 
identical  with  10  nor  14  with  20,  but  the  ratio  of  7  to 
10  is  identical  with  the  ratio  of  14  to  20,  so  that  there  is 
an  analogy  between  these  numbers.  To  multiply  two 
by  two  is  not  the  same  thing  as  to  construct  a  square 
upon  a  line  two  units  long;  but  there  is  this  analogy — 
that  there  will  be  just  as  many  units  of  area  in  the 
square  as  there  are  units  in  the  product  of  two  by  two. 
This  analogy  is  so  evident  that  we  fearlessly  assert  a 
square  mile  to  consist  of  1700  x  1760  square  yards  with- 
jut  any  trial  of  the  truth.  In  ordinary  language,  how- 
ever, analogy  has  come  to  mean  any  resemblance  be- 
tween things  which  enables  us  to  believe  of  one  what 
we  know  of  the  other. 

Thus  the  planet  Mars  possesses  an  atmosphere,  with 
clouds  and  mist  closely  resembling  our  own  ;  it  has  seas 
distinguished  from  the  land  by  a  greenish  color,  and 
polar  regions  covered  with  snow.  The  red  color  of  the 
planet  seems  to  be  due  to  the  atmosphere,  like  the  red 
color  of  our  sunrises  and  sunsets.  So  much  is  similar 
in  the  surface  of  Mars  and  the  surface  of  the  Earth  that 
we  readily  argue  that  there  must  be  inhabitants  there 
as  here.  All  that  we  can  cert-ainly  say,  however,  is, 
that  if  the  circumstances  be  really  similar,  and  similar 
germs  of  life  have  been  created  there  as  here,  there 
must  be  inhabitants.  The  fact  that  many  circum- 
stances are  similar  increases  the  probability.  But  be- 
tween the  Earth  and  the  Sun  the  analogy  is  of  a  much 
fainter  character;  we  speak  indeed  of  the  sun's  atmos- 
phere being  subject  to  storms  and  filled  with  clouds, 
but  these  clouds  are  heated  probably  beyond  the  tem* 


FORMS  OF  INDUCTION.  197 

perature  of  our  hottest  furnaces ;  if  they  produce  rain 
it  must  resemble  a  shower  of  melted  iron  ;  and  the  sun- 
spots  are  perturbations  of  so  tremendous  a  size  and 
character,  that  the  earth  together  with  half-a-dozen  of 
the  other  planets  could  readily  be  swallowed  up  in  one 
of  them.  It  is  plain  then  that  there  is  little  or  no 
analogy  between  the  Sun  and  the  Earth,  and  we  can 
therefore  with  difficulty  form  a  conception  of  anything 
going  on  in  a  sun  or  star. 

Argument  from  analogy  may  be  defined  as  direct  inductive 
inference  from  one  instance  to  any  similar  instance.  It  may,  as 
Mr.  Mill  says,  be  reduced  to  the  following  formula: — 

"  Two  things  resemble  each  other  in  one  or  more  respects  ;  a 
certain  proposition  is  true  of  the  one ;  therefore  it  is  true  of  the 
other,"  This  is  no  doubt  the  type  of  all  reasoning,  and  the  cer- 
tainty of  the  process  depends  entirely  upon  the  degree  of  resem- 
blance or  identity  between  the  cases.  In  geometry  the  cases  are 
absolutely  identical  in  all  material  points  by  hyjx)thesis,  and  no 
doubt  attaches  to  the  inference  ;  in  physical  science  the  identity 
is  a  question  of  probability,  and  the  conclusion  is  in  a  like  degree 
probable.  It  should  be  added  that  Mr.  Mill  considers  Geometri- 
cal and  Mathematical  Induction  not  to  be  properly  called  Induc- 
tion, for  reasons  of  which  the  force  altogether  escapes  my  appre- 
hension ;  but  the  reader  will  find  his  opinions  in  the  2d  chapter 
of  the  third  book  of  his  System  of  Logic. 

(2)  Reasoning  by  Examples  is  a  form  of  inductive 
inference  consisting  in  the  constant  use  of  examples 
and  instances.  The  best  way  to  describe  the  nature  of 
a  class  of  things  is  to  present  one  of  the  things  itself, 
and  point  out  the  properties  which  belong  to  the  class 
as  distinguished  from  those  peculiar  to  the  thing. 
Througnout  these  lessons,  as  throughout  every  work 
on  logic,  instances  of  propositions,  of  compound  or 


198  INDUCTION. 

complex  sentences,  of  syllogisms,  etc.,  are  continually 
used,  and  the  reader  is  asked  to  apply  to  all  similar 
cases  what  he  observes  in  the  examples  given.  It  is 
assumed  that  the  writer  selects  such  examples  as  truly 
exhibit  the  properties  in  question. 

While  all  inductive  and  analogical  inferences  rest  upon  the 
same  principles  there  are  wide  differences  between  the  sources  of 
probability.  In  analogy  we  have  two  cases  whicli  resemble  each 
other  in  a  great  many  properties,  and  we  infer  that  some  addi- 
tional property  in  one  is  probably  to  be  found  in  the  other.  The 
very  narrow  basis  of  experience  is  compensated  by  the  high  de- 
gree of  similarity.  In  the  processes  more  commonly  treated  under 
the  name  Induction,  the  things  usually  resemble  each  other  only 
in  two  or  three  properties,  and  we  require  to  have  more  instanct^a 
to  assure  us  that  what  is  true  of  these  is  probably  true  of  all 
similar  msiances.  The  less,  in  short,  the  intension  of  the  resem 
blance  the  greater  must  be  the  extension  of  our  inquiries. 

Mr.  Mill's  SyKtem  of  Logic,  Book  III,  Chap.  XX,    Of  Analogy. 
Mansel's  Aldricfi,  App.  Note  H,  On  Example  and  Analogy. 

In  this  section,  on  "  Tlie  Forms  of  Induction,*' 
we  have  considered : — 

1.  The  Character  of  the  Data. 

2.  Special  Kinds  of  Induction. 


CHAPTER    yi. 
METHOD. 

In  the  investigation  and  communication  of  truth,  we 
may  employ  various  modes  of  procedure,  some  of  which 
must  be  better  than  others.  Whatever  mode  we  em- 
ploy is  called  our  Method.  This  part  of  our  subject  is 
strictly  Applied  Logic,  being  little  more  than  the  appli- 
cation of  the  principles  already  discussed  to  the  practi- 
cal cases  of  discovery  and  exposition.  We  shall  con- 
sider Method  in  the  following  sections  under  these 
three  topics:  (1)  Indtictlve  Method;  (2)  De- 
ductive Method;  (3)  Complete  Method. 

The  Inductivp  Method  is  sometimes  called  the  Method  of  Dis- 
covery, and  sometimes  the  Analytical  Method.  It  begins  with 
facts  apparent  to  the  powers  of  observation,  and  has  tlie  difficult 
task  of  detecting  those  universal  laws  or  general  principles  which 
can  only  be  compreliended  by  intellect.  It  has  been  aptly  said 
that  the  method  of  discovery  thus  proceeds  from  tilings  better 
known  to  us  or  our  senses  {nobis  notiora),  to  those  whicli  are  more 
simple  or  better  known  in  nature  {notiora  naturce).  Tlie  Deduc- 
tive Method,  Method  of  Instruction,  or  Synthetic  Method,  pro- 
ceeds in  the  opposite  direction,  beginning  witli  the  things  notiora 
naturae,  and  proceeding  to  show  or  explain  tlie  things  ndbit 
notiora.  The  difference  is  almost  like  that  between  hiding  and 
seeking.  He  who  has  hidden  a  thing  knows  where  to  find  it ;  but 
this  is  not  the  position  of  a  discoverer,  who  lias  no  clue  except 
such  as  he  may  meet  in  his  own  diligent  and  sagacious  searcli. 

It  is  very  important  indeed  that  the  reader  should  clearly 
apprehend  the  meanings  of  Analysis  and  Synthesis.    Analysis  la 


200  METHOD. 

the  process  of  separating  a  whole  into  its  parts,  and  Synthesis 
the  combinaiiou  of  parts  into  u  whole.  The  analytical  chemist, 
who  receives  a  piece  of  mineral  for  examination,  may  be  able  to 
separate  completely  the  several  chemical  elements  of  which  it  is 
composed  and  ascertain  their  nature  and  comparative  quantities  ; 
this  is  chemical  analysis.  In  other  cases  the  chemist  mixes  to- 
gether carefully  weighed  quantities  of  certain  simple  substances 
and  combines  them  into  a  new  compound  substance ;  this  is 
chemical  synthesis.  Logical  analysis  and  synthesis  must  not  be 
confused  with  the  physical  actions,  but  they  are  nevertheless 
actions  of  mind  of  an  analogous  character. 

In  logical  synthesis  we  begin  with  the  simplest  possible 
notions  or  ideas,  and  combine  them  together.  We  have  the  best 
possible  example  in  the  elements  of  geometry.  In  Euclid  we 
begin  with  certain  simple  notions  of  points,  straight  lines, 
angles,  right  angles,  circles,  etc.  Putting  together  three  straight 
lines  we  make  a  triangle ;  joining  to  this  the  notion  of  a  right- 
angle,  we  form  the  notion  of  a  right-angled  triangle.  Joining 
four  other  equal  lines  at  right  angles  to  each  other  we  gain  the 
idea  of  a  square,  and  if  we  then  conceive  such  a  square  to  be 
formed  upon  each  of  the  sides  of  a  right-angled  triangle,  and 
reason  from  the  necessary  qualities  of  these  figures,  we  discover 
that  the  two  squares  upon  the  sides  containing  the  right  angle 
must  together  be  exactly  equal  to  the  square  upon  the  third  side, 
as  shown  in  the  47th  Proposition  of  Euclid's  first  book.  This  is 
a  perfect  instance  of  combining  simple  ideas  into  more  complex 
ones. 

We  have  often,  however,  in  Geometry  to  pursue  the  opposite 
course  of  Analysts.  A  complicated  geometrical  figure  may  be 
given  to  us,  and  we  may  have,  in  order  to  prove  the  nroperties 
which  it  possesses,  to  resolve  it  into  its  separate  parts,  and  to 
ODnsider  the  properties  of  those  parts  each  distinct  from  the 
othera 

To  express  the  difference  between  knowledge  derived  deduc- 
tively and  that  obtained  inductively,  the  Latin  phrases  n  priori 
and  (I  posteriori  are  often  used.  By  A  priori  reasoning  we  mean 
argument  based  on  truths  previously  known  ;  A  posteriori  rea- 
•oning,  on  the  contrary,  proceeds  to  infer  from  the  consequences 


INDUCTIVE  METHOD.  201 

of  a  general  truth  what  that  general  truth  is.  Many  philosophers 
consider  that  the  mind  is  naturally  in  possession  of  certain  lawg 
or  truths  which  it  must  recognize  in  every  act  of  thought ;  all 
Buch,  if  they  exist,  would  be  d  priori  truths.  It  cannot  be 
doubted,  for  instance,  that  we  must  always  recognize  in  thought 
the  three  Primary  Laws  of  Thought.  We  have  there  an  ((  piiori 
knowledge  that  "  matter  cannot  both  have  weight  and  be  without 
weight,"  or  that  "every  thing  must  be  either  self-luminous  or 
not  self-luminous."  But  there  is  no  law  of  thought  which  can 
oblige  us  to  think  that  matter  has  weight,  and  luminous  ether 
has  not  weight ;  that  Jupiter  and  Venus  are  not  self-luminous, 
but  that  comets  are  to  some  extent  self-luminous.  These  are 
facts  which  are  no  doubt  necessary  consequences  of  the  laws  of 
nature  and  the  general  constitution  of  the  world ;  but  as  we  are 
not  naturally  acquainted  with  all  the  secrets  of  creation,  we  have 
to  learn  them  by  observation,  or  by  the  d  posteriori  method. 


SBOTIOIT    I- 

INDUCTIVE    METHOD. 

1.  The  Search  for  Facts. 

All  knowledge,  it  may  be  safely  said,  must  be  ulti- 
mately founded  upon  experience,  which  is  but  a  general 
name  for  the  various  feelings  impressed  upon  the  mind 
at  any  period  of  its  existence.  The  mind  never  creates 
entirely  new  knowledge  independent  of  experience,  and 
all  that  the  reasoning  powers  can  do  is  to  arrive  at  the 
full  meaning  of  the  facts  which  are  in  our  possession. 
In  previous  centuries  men  of  the  highest  ability  have 
held  that  the  mind  of  its  own  power  alone  could,  by 
Buflficient  cogitation,  discover  what  things  outside  us 


*402  METHOD. 

should  be,  and  would  be  found  to  be  on  examination. 
They  thought  that  we  were  able  to  anticipate  Natun 
by  evolving  from  the  human  mind  an  idea  of  what 
things  would  be  made  by  the  Creator.  The  celebrated 
pbilosopher  Descartes  thus  held  that  whatever  the 
mind  can  clearly  conceive  may  be  considered  true  ;  but 
we  can  conceive  the  existence  of  mountains  of  gold  or 
oceans  of  fresh  water,  wliich  do  not  as  a  fact  exist. 
Anything  that  we  can  clearly  conceive  must  be  con- 
formable to  the  laws  of  thought,  and  its  existence  is 
then  not  impossible,  so  far  as  our  intellect  is  concerned ; 
but  the  forms  and  sizes  and  manners  in  which  it  has 
pleased  the  Creator  to  make  things  in  this  or  any  other 
part  of  the  universe,  cannot  possibly  be  anticipated  by 
the  exceedingly  limited  wisdom  of  the  human  mind, 
and  can  only  be  learnt  by  actual  examination  of  exist- 
ing things. 

In  the  latter  part  of  the  13th  century  the  great  Roger  Bacon 
clearly  taught  in  England  the  supremo  imiwrtanco  of  exjierience 
as  the  basis  of  knowledge;  but  the  same  doctrine  was  also,  by  a 
curious  coincidence,  again  uplield  in  the  17th  century  by  the 
great  Chancellor  Francis  Bacon,  after  whom  it  has  been  called 
the  Baconian  Philosophy.  I  believe  tliat  Roger  Bacon  was  even 
a  greater  man  than  Francis,  whose  fame  is  best  known  ;  but  the 
words  in  which  Francis  Bacon  procleimod  the  imjwrtance  of 
experience  and  experiment  must  lie  ever  memorable.  In  the 
beginning  of  his  great  worK,  the  Novum  Organum,  or  New  In- 
tlrument,  he  thus  points  out  our  proper  position  as  learners  in 
the  world  of  nature. 

"  Man,  the  Servant  and  Interpreter  of  Nature,  can  do  and 
understand  as  much  as  he  has  ol)servi'd  concerning  the  order  of 
nature  in  outward  things  or  in  the  mind  ;  more,  he  can  neither 
know  nor  do." 

Tho  alK>vc  is  the  first  of  the  aphorisms  or  paragraphs  witb 


INDUCTIVE   METHOD.  203 

which  the  Ifovum  Organum  commences.  In  the  second  aphorism 
lie  asserts  that  the  unaided  mind  can  effect  little  and  is  liable  tc 
err ;  assistance  in  the  form  of  a  definite  logical  metliod  is  requi- 
site, and  this  it  was  the  purpose  of  his  New  Instrument  to  fur- 
nish. The  8d  and  4th  aphorisms  must  be  given  entire ;  they 
are: — 

"  Human  science  and  human  power  coincide,  because  ignorance 
of  a  cause  deprives  us  of  the  effect.  For  nature  is  not  conquered 
except  by  obedience ;  and  what  we  discover  as  a  cause  by  con- 
templation becomes  a  rule  in  operation." 

"Man  can  himself  do  nothing  else  than  move  natural  bodies 
to  or  from  each  other ;  nature  working  within  accomplishes  the 
rest." 

Thus  we  see  that  the  first  essential  in  the  inductive 
method  is  a  knowledge  of  facts.  This  is  obtained  in 
two  ways: 

(1)  By  Observation.  -  To  observe  is  merely  to  notice 
events  and  changes  which  are  produced  in  the  ordinary 
course  of  nature,  without  being  able,  or  at  least  attempt- 
ing, to  control  or  vary  those  changes.  Thus  the  ciirly 
astronomers  observed  the  motions  of  the  sun,  moon 
and  planets  among  the  fixed  stars,  and  gradually  de- 
tected many  of  the  laws  or  periodical  returns  of  those 
bodies.  Thus  it  is  that  the  meteorologist  observes  the 
ever-changing  weather,  and  notes  the  height  of  the 
barometer,  the  temperature  and  raoistness  of  the  air, 
the  direction  and  force  of  the  wind,  the  height  and 
character  of  the  clouds,  without  being  in  the  least  able 
to  govern  any  of  these  facts.  The  geologist  again  is 
generally  a  simple  observer  when  he  investigates  the 
nature  and  position  of  rocks.  The  zoologist,  the  bota- 
nist, and  the  mineralogist  usually  employ  mere  observa- 
tion when    they    examine    the    animals,   plants,   and 


204  METHOD. 

minerals,  as  they  are  met  with  in  their  natural  condi 
tion. 

(2)  By  Experiment. — In  experiment,  on  the  contrary, 
we  vary  at  our  will  the  combinations  of  things  and  cir- 
cumstances, and  then  observe  the  result.  It  is  thus 
that  the  chemist  discovers  the  composition  of  water  by 
using  an  electric  current  to  separate  its  two  constituents, 
oxygen  and  hydrogen.  The  mineralogist  may  employ 
experiment  when  he  melts  two  or  three  substances 
together  to  ascertain  how  a  particular  mineral  may 
have  been  produced.  Even  the  botanist  and  zoologist 
are  not  confined  to  passive  observation  ;  for  by  remov- 
ing animals  or  plants  to  different  climates  and  different 
Boils,  and  by  what  is  called  domestication,  they  may 
try  how  far  the  natural  forms  and  species  are  capable 
of  alteration. 

It  is  obvious  that  experiment  is  the  most  potent  and 
direct  mode  of  obtaining  facts  where  it  can  be  applied. 
We  might  have  to  wait  years  or  centuries  to  meet 
wjcidentally  with  facts  which  we  can  readily  produce  at 
any  moment  in  a  laboratory ;  and  it  is  probable  that 
most  of  the  chemical  substances  now  known,  and  many 
excessively  nseful  products,  would  never  have  been  dis- 
covered at  all  by  waiting  till  nature  presented  them 
spontaneously  to  our  observation.  Many  forces  and 
changes  too  may  go  on  in  nature  constantly,  but  in  so 
slight  a  degree  as  to  escape  our  senses,  and  render  some 
experimental  means  necessary  for  their  detection.  Elec- 
tricity doubtless  operates  in  every  particle  of  matter, 
|x?rhap3  at  every  moment  of  time;  and  even  the  ancients 
could  not  but  notice  its  action  in  the  loadstone,  in 
lightning,  in  the  Aurora  Borealis,  or  in  a  piece  o2 


INDUCTIVE  METHOD,  205 

robbed  amber  (electrum).  But  in  lightning  electricity 
was  too  intense  and  dangerous;  in  the  otlier  csises  it 
was  too  feeble  to  be  properly  understood.  The  science 
of  electricity  and  magnetism  could  only  advance  by 
getting  regular  supplies  of  electricity  from  the  common 
electric  machine  or  the  galvanic  battery,  and  by  making 
powerful  electro-magnets.  Most  if  not  all  the  effects 
which  electricity  produces  must  go  on  in  nature,  but 
altogether  too  obscurely  for  observation. 

Experiment,  again,  is  rendered  indispensable  by  tho 
fact  that  on  the  surface  of  the  earth  we  usually  meet 
substances  under  certain  uniform  conditions,  so  that 
we  could  never  learn  by  observation  what  would  be  the 
nature  of  such  substances  under  other  conditions.  Thus 
carbonic  acid  is  only  met  in  the  form  of  a  gas,  proceed- 
ing from  the  combustion  of  carbon  ;  but  when  exposed 
to  extreme  pressure  and  cold,  it  is  condensed  into  a 
liquid,  and  may  even  be  converted  into  a  snow-like 
solid  substance.  Many  other  gases  have  in  like  manner 
been  liquefied  or  solidified ;  and  there  is  reason  to  be- 
lieve that  every  substance  is  capable  of  taking  all  the 
three  forms  of  solid,  liquid  and  gas,  if  only  the  condi- 
tions of  temperature  and  pressure  can  be  sufficiently 
varied.  Mere  observation  of  nature  would  have  led  us, 
on  the  contrary,  to  suppose  that  nearly  all  substances 
were  fixed  in  one  condition  only,  and  could  not  be  con- 
verted from  solid  into  liquid  and  from  liquid  into  gas. 

It  must  not  be  supposed,  however,  that  we  can  draw  any  pre- 
cise line  between  observation  and  experiment,  and  say  where 
the  one  ends  and  the  other  begins.  The  difference  is  ratlier  one 
of  degree  than  of  kind  ;  and  all  we  can  say  is  that  the  more  we 
vary  the  conditions  artificially  the  more  we  employ  experiment 


S06  METHOD. 

I  have  said  that  meteorology  is  a  science  of  nea/rly  pare  observa- 
tion, but  if  we  purposely  ascend  inountaius  to  observe  the  rare- 
faction  aad  cooling  of  tlie  atmosphere  by  elevation,  or  if  vre  make 
balloon  ascents  for  the  same  purpose,  like  Gay  Lussac  and 
Glaisher,  we  so  vary  the  mode  of  observation  as  almost  to  rendei 
it  experimental.  Astronomers  again  may  almost  be  said  to  ex- 
periment instead  of  merely  observing  when  they  simultaneously 
employ  instruments  as  far  to  the  north,  and  as  far  to  the  south, 
upon  the  earth's  surface  as  j  ossible,  in  order  to  observe  the  ap- 
parent difference  of  place  of  Venus  when  crossing  the  sun  in  a 
transit  so  as  thus  to  compare  the  distances  of  Venus  and  the  sun 
with  the  dimensions  of  the  earth. 

2.  The  Rule  for  Observation. 

Logic  can  give  little  or  no  aid  in  making  an  acute  or 
accurate  observer.  There  are  no  delinitc  rnles  which 
can  be  laid  down  upon  the  subject.  To  observe  well  is 
an  art  which  can  only  be  acquired  by  practice  and 
training  ;  and  it  is  one  of  the  greatest  advantages  of  the 
pursuit  of  the  Natural  Sciences  that  the  faculty  of  clear 
and  steady  observation  is  thereby  cultivated.  Logic 
can,  however,  give  us  this  caution,  wliich  has  been  well 
pointed  out  by  Mr.  Mill — to  discriminate  accurately 
between  what  we  really  do  observe  and  what  we  only 
infer  from  the  facts  observed.  So  long  as  we  only 
record  and  describe  what  our  senses  have  actually 
tritnessed,  we  cannot  commit  an  error ;  but  Iho  moment 
we  presume  or  infer  anything  we  are  lial)lo  to  mistake. 
For  instance,  we  examine  the  sun's  surface  with  a  tele- 
scope and  observe  that  it  is  intensely  bright  except 
where  there  are  small  breaks  or  circular  openings  in 
the  surface  with  a  dark  interior.  We  are  iri-osistibly 
led  to  the  conclusion  that  the  inside  of  the  sun  is  colder 
ind  darker  than  the  outside,  and  record  as  a  fact  that 


INDUCTIVE   METHOl,.  207 

we  saw  the  dark  interior  of  the  sun  through  certain 
openings  in  its  luminous  atmosphere.  Such  a  record, 
however,  would  involve  mistaken  inference,  for  we  saw 
nothing  but  dark  spots,  and  we  should  not  have  done 
more  in  observation  than  record  the  shape,  size,  appear- 
ance and  change  of  such  spots.  Whether  they  are  dark 
clouds  above  the  luminous  surface,  glimpses  of  the  dark 
interior,  or,  as  is  now  almost  certainly  inferred,  something 
entirely  different  from  either,  can  only  be  proved  by  a 
comparison  of  many  unprejudiced  observations. 

The  reader  cannot  too  often  bear  in  min*"!  the  caution 
against  confusing  facts  observed  with  infepe.ices  from 
those  facts.  It  is  not  too  much  to  say  that  nin*^-tenths 
of  what  we  seem  to  see  and  hear  is  inferred,  not  nally 
felt.  Every  sense  possesses  what  are  called  acquired 
perceptions,  that  is,  the  power  of  judging  unconsciously, 
by  lon^  experience,  of  many  things  which  cannot  be 
the  objects  of  direct  perception.  The  eye  cannot  see 
distance,  yet  "we  constantly  imagine  and  say  that  we 
gee  things  at  such  and  such  distances,  unconscious  that 
it  is  the  result  of  judgment.  As  Mr.  Mill  remarks,  it  is 
too  much  to  say  *'I  saw  my  brother."  All  I  positively 
know  is  that  I  saw  some  one  who  closely  resembled  my 
brother  as  far  as  could  be  observed.  It  is  by  judg- 
ment only  I  can  assert  he  was  my  brother,  and  thai 
judgment  may  possibly  be  wrong. 

Nothing  is  more  important  in  observation  and  experi- 
ment than  to  be  uninfluenced  by  any  prejudice  or  theory 
in  correctly  recording  tlie  facts  observed  and  allowing 
to  them  their  proper  weight.  He  who  does  not  do  so 
will  almost  always  be  able  to  obtain  facts  in  support  oi 
an  opinion  however  erroneous. 


208  METHOD. 

8*  The  Uses  of  Hypothesis  and  Theory. 

In  order  to  carry  on  observation  and  experiment  sue 
cessfully,  it  is  frequently  necessary  to  form  some  hypo- 
thesis, or  tlieory,  to  direct  the  course  of  inquiry.  We 
^vill  therefore  notice  these  forms  of  supposition  mora 
particularly. 

(1)  Hypothesis  is  derived  from  the  Greek  words  vtt6^ 
under,  and  Oioig,  placing,  and  is  therefore  exactly 
synonymous  with  the  Latin  word  suppositio,  a  placing 
under,  whence  our  common  word  supposition.  It  ap- 
peal's to  mean  in  science  the  imagining  of  some  thing, 
force  or  cause,  which  underlies  the  phenomena  we  are 
examining,  and  is  the  agent  in  their  production  with- 
out being  capable  of  direct  observation.  In  making 
a  hypothesis  we  assert  the  existence  of  a  cause  on  the 
ground  of  the  effects  observed,  and  the  probability 
of  its  existence  depends  upon  the  number  of  diverse 
facts  or  partial  laws  that  wo  are  thus  enabled  to  ex« 
nlain  or  reduce  to  harmony.  To  be  of  any  value  at  all 
a  hypothesis  must  harmonize  at  least  two  different 
facts.  If  we  account  for  the  effects  of  opium  by  sa}ing 
urith  Moliere  that  it  possesses  a  dormitive  power,  or  say 
that  the  magnet  atliiucts  because  it  has  a  vmgnetie 
power,  every  one  can  see  that  we  gain  nothing.  We 
know  neither  more  nor  less  about  the  dormitive  or 
magnetic  power  than  we  do  about  opium  or  the  mag- 
net. But  if  we  suppose  the  magnet  to  attract  because 
it  is  occupied  by  circulating  currents  of  electricity  the 
hypothesis  may  seem  a  very  improbable  one.  but  ia 
valid,  because  we  thus  draw  a  certain  analogy  between 
a  magnet  and  a  coil  of  wire  conveying  electricity.  Such 


INDUCTIVE   METHOD.  809 

a  coil  of  wire  attracts  other  coils  exactfy  in  the  way  that 
one  magnet  attracts  another ;  so  that  this  hypothesis 
enables  us  to  harmonize  several  different  facts.  The  ex- 
istence of  intense  heat  in  the  interior  of  the  earth  is  hypo- 
thetical in  so  far  as  regards  the  impossibility  of  actually 
seeing  and  measuring  the  heat  directly,  but  it  harmo. 
nizes  so  many  facts  derived  from  different  sources  that 
we  can  hardly  doubt  its  existence.  Thus  the  occurrence 
of  hot  springs  and  volcanoes  are  some  facts  in  its  favor, 
though  they  might  be  explained  on  other  grounds ;  the 
empirical  law  that  the  heat  increases  as  we  sink  mines 
in  any  part  of  the  earth's  surface  is  stronger  evidence. 
The  intensely  heated  condition  of  the  sun  and  other 
stars  is  strongly  confirmatory  as  showing  that  other 
bodies  do  exist  in  the  supposed  condition  of  the  earth's 
interior.  The  cool  state  of  the  earth's  surface  is  per- 
fectly consistent  with  its  comparatively  small  size  and 
the  known  facts  and  laws  concerning  the  conduction 
and  radiation  of  heat.  And  the  more  we  learn  con- 
cerning the  way  in  which  the  sun's  heat  is  supplied  by 
the  fall  of  meteoric  matter,  the  more  it  is  probable  that 
the  earth  may  have  been  intensely  heated  like  the  sun 
at  some  former  time,  although  for  an  immense  period 
ic  has  been  slowly  growing  colder.  A  supposition 
coinciding  with  so  many  facts,  laws,  and  other  probable 
hypotheses,  almost  ceases  to  be  hypothetical,  and  its 
high  probability  causes  it  to  be  regarded  as  a  known 
fact. 

Provided  it  is  consistent  with  the  laws  of  thought  there  is 
nothing  that  we  may  not  have  to  accept  as  a  probable  hypothesis, 
however  difficult  it  may  be  to  conceive  and  understand.  The 
force  of  gravity  is  hypothetical  in  so  far  that  we  know  it  only  b^ 


210  METHOD. 

its  effects  upon  the  motions  of  bodies.  Its  decrease  at  a  distanoi 
iiarmonizes  exactly  indeed  with  the  way  in  which  light,  sound, 
electric  or  magnetic  attractions,  and  in  fact  all  influences  which 
emanate  from  a  point  and  spread  through  space,  decrease  ;  hence 
it  is  probable  that  the  law  of  the  inverse  square  is  absolutely 
true.  But  in  other  respects  gravity  is  strongly  opposed  to  all  our 
ideas.  If  sound  could  travel  to  the  sun  as  rapidly  as  in  the 
aarth's  atmosphere  it  would  require  nearly  fourteen  years  to 
reach  its  destination;  were  the  sun  and  earth  united  by  a  solid 
continuous  bar  of  iron,  a  strong  pull  at  one  end  would  not  be  felt 
at  the  other  until  nearly  three  years  had  passed.  Light  indeed 
comes  from  the  sun  in  rather  more  tiian  eight  minutes  ;  but  what 
are  we  to  think  of  the  force  of  gravity,  which  appears  to  reach 
the  sun  in  an  instant — so  short  that  no  calculations  have  yet  been 
able  to  detect  any  interval  at  all?  In  fact  there  seems  some 
reason  to  suppose  that  gravity  is  felt  instantaneously  throughout 
the  immeasurable  regions  of  space. 

{%)  The  word  Theory  has  constantly  been  used  in  the 
last  few  lessons,  and  deserves  some  examination.  It 
comes  from  the  Greek  Oei^pia,  meaning  contemplation, 
reflection  or  speculation  ;  but  this  gives  us  little  clue  to 
its  modern  use.  In  reahty  the  word  is  highly  am- 
biguous, being  sometimes  used  as  equivalent  to  hypo- 
thesis, at  other  times  as  equivalent  to  general  law  or 
truth.  When  people  form  theories  concerning  comets, 
the  sun,  the  cause  of  earthquakes,  etc.,  they  imagine  a 
great  many  things  which  may  or  may  not  exist ;  such 
theories  are  really  complicated  hypotheses,  and  should 
be  so  called.  In  this  sense  there  are  two  theories  of 
electricity,  one  of  which  supposes  the  existence  of  a 
single  fluid  which  accumulates  in  some  places  and  has 
then  a  tendency  to  discharge  itself  towards  places  where 
there  is  a  deficiency,  just  as  water  always  tends  to  find 
its  level ;  the  other  supposes  the  existence  of  two  fluidv 


IKDUCTIVE  METHOD.  211 

jehich  are  commonly  united,  but  when  separated  tend 
to  rush  back  into  union  again.  These  so-called  theories 
are  really  hypotheses,  because  we  have  no  independent 
evidence  of  the  existence  of  any  fluid,  and  it  is  now 
almost  certain  that  there  is  no  such  thing.  The  atomic 
theory,  again,  is  really  a  hypothesis  suggested  by  Dal- 
ton  to  explain  the  remarkable  laws  which  he  detected 
in  the  proportions  of  chemical  elements  which  com- 
bine together.  It  is  a  valid  hypothesis  in  so  far 
as  it  does  really  explain  the  fixedness  of  the  quantities 
which  combine;  but  it  is  purely  hypothetical  as  regards 
the  shapes,  properties  or  absolute  magnitudes  of  the 
atoms,  because  we  have  no  facts  which  it  can  harmonize 
in  these  respects,  and  no  apparent  means  of  gaining 
them. 

In  another  and  more  proper  sense  theory  is  opposed 
to  practice,  just  as  the  general  is  opposed  to  the  par- 
ticular. The  theory  of  gravitation  means  all  the  more 
general  laws  of  motion  and  attraction  on  which  New- 
ton founded  his  system  of  the  Universe.  We  may 
know  what  those  laws  are  without  being  able  to 
determine  the  place  of  a  planet  or  make  any  prac- 
tical use  of  them ;  the  particular  results  must  be 
calculated  out  by  skilful  astronomers  before  navi- 
gators, travellers  or  others  can  make  practical  use  of 
them  in  the  determination  of  the  latitude  or  longi- 
tude. When  we  speak  of  the  mathematical  theory 
of  sound,  the  lunar  theory,  the  theory  of  the  tides, 
the  word  is  employed  without  any  special  reference 
to  hypotliesis,  and  is  merely  equivalent  to  general 
knowledge  or  science,  implying  t!ie  possession  of  a 
complete  series  of  general  and  accurate  laws,  but  in  no 


tl2  METHOD. 

way  distinguishing  them  from  accurate  knowledge  in 
general.  When  a  word  is  really  used  in  an  equivocal 
manner  like  theory,  it  is  not  desirable  to  attempt  to 
give  it  an  accurate  definition  which  would  be  imagi* 
nary  and  artificial. 

4.  Definitions  of  Terms  Employed  in 
Investigatiuu. 

It  is  important  that  the  learner  should  have  precise 
ideas  of  the  meaning  of  the  following  words  employed 
in  the  investigation  of  truth,  and  accordingly  these 
definitions  are  introduced  at  this  point. 

(1)  The  word  Fact  is  used  very  often  in  this  as  in 
most  books,  and  demands  a  few  remarks.  It  is  derived 
from  factum^  the  past  participle  of  facerey  to  do,  and 
would  thus  mean  something  which  is  done,  an  act,  or 
deed  ;  but  the  meaning  is  evidently  greatly  extended  by 
analogy.  We  usually  oppose  to  each  other  fact  and 
theory,  but  just  as  theory  seems  to  have  two  ambiguous 
meanings,  so  I  believe  that  fact  is  ambiguous.  Some- 
times it  means  what  is  certain  and  known  by  the  evi- 
dence of  the  senses,  as  opposed  to  what  is  known  only 
probably  by  hypothesis  and  inference  ;  at  other  times  it 
js  contrasted  to  a  general  law,  and  is  equivalent  to  a 
particular  instance  or  case.  A  law  of  great  generality 
may  often  be  as  certain  and  true,  especially  in  mathe- 
matics, as  the  particular  facts  coming  under  it,  so  that 
the  contrast  must  in  this  case  be  that  between  the 
general  and  particular.  We  often  use  the  word  too  in 
common  life,  as  merely  equivalent  to  fruih  ;  thus  we 
might  say,  "  It  is  a  fact  that  the  primary  laws  of 
thought  are  the  foundation  of 'reasoning."     In  short,  as 


INDUCTIVE  METHOD.  213 

theory  means  ambiguously  what  is  hypothetical,  general, 
abstract,  or  uncertain,  so  fact  is  equally  ambiguous, 
and  means  confusedly  what  is  intuitively  known,  par 
ticular,  concrete  or  certain. 

(2)  The  word  Phenomenon  will  also  be  often  used. 
It  means  simply  anything  which  appears,  and  is  there- 
fore observed  by  the  senses ;  the  derivation  of  the 
word  from  the  Greek  word  <f>aiv6nevov,  that  which  ap- 
pears, exactly  corresponds  to  its  logical  use. 

(3)  By  the  Cause  of  an  event  we  mean  the  circum. 
stances  which  must  have  preceded  in  order  that  the 
event  should  hai)pen.  Nor  is  it  generally  possible  to 
say  that  an  event  has  one  single  cause  and  no  more. 
There  are  usually  many  different  things,  conditions  or 
circumstances  necessary  to  the  production  of  an  effect, 
and  all  of  them  must  be  considered  causes  or  necessary 
parts  of  the  cause.  Thus  the  cause  of  the  loud  explo- 
sion in  a  gun  is  not  simply  the  pulling  of  the  trigger, 
which  is  only  the  last  apparent  cause  or  occasicn  of  the 
explosion  ;  the  qualities  of  the  powder,  the  proper  form 
of  the  barrel,  the  existence  of  some  resisting  charge, 
the  proper  arrangement  of  the  percussion  cap  and 
powder,  the  existence  of  a  surrounding  atmosphercj 
are  among  the  circumstances  necessary  to  the  loud  re- 
port of  a  gun  ;  any  of  them  being  absent  it  would  nol 
have  occurred. 

(4)  The  learner  will  perhaps  have  noticed  the  fre- 
quent use  of  the  word  Tendency,  and  I  have  repeatedly 
spoken  of  a  cause  as  tending  to  produce  its  effect.  If 
the  joint  and  homogeneous  action  of  causes  has  been 
clearly  explained,  it  will  now  be  clear  that  a  tendency 
means  a  cause  which  will  produce  an  effect  unless  thera 


314  METHOD 

be  opposite  causes,  which,  in  combinatior.  with  i^ 
counteract  and  disguise  that  effect.  Thus  when  we 
throw  a  stone  into  the  air  the  attractive  power  of  the 
earth  tends  to  make  it  fall,  but  the  upward  motion  we 
have  impressed  upon  it  disguises  the  result  for  a  certain 
time.  The  interminable  revolving  motion  of  the  moon 
round  the  earth  is  the  result  of  two  balanced  tendencies, 
that  towards  the  earth,  and  that  to  proceed  onward  in 
a  straight  line.  The  laws  of  motion  and  gravity  are 
such  that  this  balance  must  always  be  preserved ;  if  the 
moon  by  any  cause  were  brought  nearer  to  the  earth  its 
tendency  to  fly  off  would  be  increased,  and  wonld  ex- 
ceed the  effect  of  gravity  until  it  had  regained  its  proper 
distance.  A  tendency  then  is  a  cause  which  may  or 
may  not  be  counteracted. 

(5)  By  an  Antecedent  we  mean  any  thing,  condition, 
or  circumstance  which  exists  before  or,  it  may  De,  at 
the  same  time  with  an  event  or  phenomenon.  J3y  a 
Consequent  we  mean  any  thing,  or  circumstance,  event, 
or  phenomenon,  which  is  different  from  any  of  the 
antecedents  and  follows  after  their  conjunction  or  put- 
ting together.  It  does  not  follow  that  an  antecedent  is 
a  cause,  Ijecause  the  effect  might  have  happened  with- 
out it.  Thus  the  sun's  light  may  be  an  antecedent  to 
the  burning  of  a  house,  but  not  the  cause,  because  the 
house  would  bum  equally  well  in  the  night.  A  neces- 
sary or  indispensable  antecedent  is,  however,  identical 
with  a  cause,  being  that  without  which  the  effect  would 
not  take  place. 

(G)  A  Law  is  a  uniform  mode  of  sequence,  or  rule  of 
action.  The  laws  of  nature  are  universal  modes  of 
sequence,  or  general  expressions  for  the  order  of  phe- 


INDUCTIVE   METHOD.  215 

nomena.     They  are  not  causes,  but  the  rules  according 
to  which  causes  act. 

5.  Canons  of  Induction. 

Mr.  Mill  has  laid  down  several  rules,  or  canons,  for 
the  inductive  determination  of  the  laws  of  nature. 
These  rules  express  certain  methods  of  induction. 

(1)  The  first  method  of  induction  is  tliat  which  Mr. 
Mill  has  aptly  called  the  Method  of  agreement.  It  de- 
pends upon  the  rule  that  '*  If  two  or  more  instances  of 
the  phenomenon  under  investigation  have  only  one  cir- 
cumstance in  common,  the  circumstance  in  which  alone 
all  the  instances  agree,  is  the  cause  (or  effect)  of  the 
given  phenomenon."  The  meaning  of  this  First  Canon 
of  inductive  inquiry  might,  I  think,  be  more  briefly 
expressed  by  sajring  that  the  sole  invariable  antecedent 
if  a  phenomenon  is  probably  its  cause. 

To  apply  this  method  we  must  collect  as  many  in- 
stances of  the  phenomenon  as  possible,  and  compare 
together  their  antecedents.  Among  these  the  causes 
will  lie,  but  if  we  notice  that  certain  antecedents  are 
present  or  absent  without  appearing  to  affect  the  result, 
we  conclude  that  they  cannot  be  necessary  antecedents. 
Hence  it  is  the  one  antecedent  or  group  of  antecedents 
always  present,  when  the  effect  follows,  that  we  con- 
sider the  cause.  For  example,  bright  prismatic  colors 
are  seen  on  bubbles,  on  films  of  tar  floating  upon  water, 
on  thin  plates  of  mica,  as  also  on  cracks  in  glass,  or 
between  two  pieces  of  glass  pressed  together  On  ex- 
amining all  such  cases  they  seem  to  agree  in  nothing 
but  the  presence  of  a  very  thin  layer  or  plate,  and  it 
appears  to  make  no  appreciable  difference  of  what  kind 


'^16  METHOD. 

of  matter,  solid,  liquid,  or  gaseous,  the  plate  is  made. 
Hence,  we  conclude  that  such  colors  are  caused  merely 
by  the  thinness  of  the  plates,  and  this  conclusion  is 
proved  true  by  the  theory  of  the  interference  of  light. 
Sir  David  Brewster  beautifully  proved  in  a  similar  way 
that  the  colors  seen  upon  mother-of-pearl  are  not  caused 
by  the  nature  of  the  substance,  but  by  the  form  of  the 
surface.  He  took  impressions  of  the  mother-of-pearl 
in  wax,  and  found  that  although  tlie  substance  wa? 
entirely  different  the  colors  were  exactly  the  same. 
And  it  was  afterwards  found  that  if  a  plate  of  metal 
had  a  surface  marked  by  very  fine  close  grooves,  it 
would  have  iridescent  colors  like  those  of  mother-of- 
pearl.  Hence  it  is  evident  that  the  form  of  the  sur- 
face, which  is  the  only  invariable  antecedent  or  condi- 
tion requisite  for  the  production  of  the  colors,  must  be 
their  cause. 

The  method  of  agreement  is  subject  to  a  serioiia  diflBculty, 
called  by  Mr.  Mill  the  Plurality  of  Causes,  consisting  in  the  fact 
that  the  same  effect  may  in  different  instances  be  owing  to  differ- 
ent causes.  Thus  if  we  inquire  accurately  into  the  cause  of  heat 
we  find  that  it  is  produced  by  friction,  by  burning  or  combustion, 
by  electricity,  by  pressure,  etc.;  so  that  it  does  not  follow  that  if 
there  happened  to  be  one  and  the  same  thing  present  in  all  the 
cases  we  examined  this  would  be  the  cause. 

(2)  The  second  method  of  induction  which  we  will 
now  consider  is  free  from  this  difficulty,  and  is  known 
as  the  Method  of  Difference.  It  is  stated  in  Mr.  Mill's 
Second  Canon  aa  follows:— 

"  If  an  instance  in  which  the  phenomenon  under  in- 
vestigation occurs,  and  an  instance  in  which  it  does  not 
occur,  have  every  circumstance  in  common  save  one, 


INDUCTIVE   METHOD.  217 

that  one  occurring  only  in  the  former,  the  circum- 
stance in  which  alone  the  two  instances  differ,  is  the 
effect,  or  the  cause,  or  an  indispensable  part  of  the 
cause,  of  the  phenomenon.*' 

In  other  words,  we  may  say  that  the  antecedent  which 
is  invariably  present  when  the  phenomenon  follows, 
and  invariably  absent  when  it  is  absent,  other  circum- 
stances remaining  the  same,  is  the  cause  of  the  phe- 
nomenon in  those  circumstances. 

Thus  we  can  clearly  prove  that  friction  is  one  cause 
of  heat,  because  when  two  sticks  are  rubbed  together 
they  become  heated ;  when  not  rubbed  they  do  not  be- 
come heated.  Sir  Humphrey  Davy  showed  that  even 
two  pieces  of  ice  when  rubbed  together  in  a  vacuum 
produce  heat,  as  shown  by  their  melting,  and  thus  com- 
pletely demonstrated  that  the  friction  is  the  source  and 
cause  of  the  heat.  We  prove  that  air  is  the  cause  of 
sound  being  communicated  to  our  ears  by  striking  a 
Oell  in  the  receiver  of  an  air-pump,  as  Hawksbee  first 
did  in  1705,  and.  then  observing  that  when  the  receiver 
is  full  of  air  we  hear  the  bell ;  when  it  contains  little  or 
no  air  we  do  not  hear  the  bell.  We  learn  that  sodium 
or  any  of  its  compounds  produces  a  spectrum  having 
a  bright  yellow  double  line  by  noticing  that  there  is  no 
such  line  in  the  spectrum  of  light  when  sodium  is  not 
present,  but  that  if  the  smallest  quantity  of  sodium  be 
thrown  into  the  flame  or  other  source  of  light,  the 
bright  yellow  line  instantly  appears  Oxygen  is  the 
cause  of  respiration  and  life,  because  if  an  animal  be 
put  into  a  jar  full  of  atmospheric  air,  from  which  the 
oxygen  has  been  withdrawn,  it  soon  becomes  suffocated. 

This  is  essentially  the  great  method  of  experiment,  and  ita 
10 


218  METHOD. 

utility  mainly  depends  upon  the  precaution  of  only  varying  otm 
circuTiviiaiice  at  a  time,  all  other  circumdanees  being  maintained 
just  as  they  were.  This  is  expressed  in  one  of  the  rules  for  con- 
ducting experiments  given  by  Thomson  and  Tait  in  their  great 
treatise  on  Natural  Philosophy,  Vol.  I,  p.  307,  as  follows  :-^ 

"  In  ail  oases  when  a  particular  agent  or  cause  is  to  be  studied, 
experiments  should  be  arranged  in  such  a  way  as  to  lead  if  pos- 
sible to  results  dejiending  on  it  alone  ;  or,  if  this  cannot  be  done, 
they  should  be  arranged  so  as  to  increase  the  effects  due  to  the 
cause  to  be  studied  till  these  so  far  exceed  the  unavoidable  con- 
comitants, that  the  latter  may  be  considered  as  only  disturbing, 
not  essentially  modifying,  the  effects  of  the  principal  agent." 

It  would  be  an  imperfect  and  unsatisfactory  experiment  to 
take  air  of  whicli  the  oxygen  has  been  converted  into  carbonic 
acid  by  the  burning  of  carbon,  and  argue  that,  because  an  animal 
dies  in  sucli  air,  oxygen  is  the  cause  of  respiration.  Instead  of 
merely  withdrawing  the  oxygen  we  have  a  new  substance,  car- 
bonic acid,  present,  which  is  quite  capable  of  killing  the  animal 
by  its  own  poisonous  properties.  Tlie  animal,  in  fact,  would  be 
suffocated  even  when  a  considerable  proportion  of  oxygen  re- 
mained, so  that  the  presence  of  the  carbonic  acid  is  a  disturbin^f 
circumstance  which  confuses  and  vitiates  the  experiment. 

It  is  ]X)ssible  to  prove  the  existence,  and  even  to  measure  the 
amount  of  the  force  of  gravity,  by  delicately  suspending  a  small 
ball  about  the  size  of  a  marble  and  then  suddenly  bringing  a  very 
heavy  leaden  ball  weighinjif  a  ton  or  more  close  to  it.  The  small 
ball  will  be  attracted  and  set  in  motion ;  but  the  experiment 
would  not  be  of  the  least  value  unless  performed  with  the  utmost 
precaution.  It  is  obvious  that  the  sudden  motion  of  the  large 
leaden  ball  would  disturb  the  air,  shake  the  room,  cause  currents 
in  the  air  by  its  coldness  or  warmth,  and  even  occasion  electric 
attractions  or  repulsions ;  and  these  would  probably  disturb  the 
small  ball  far  more  than  the  force  of  gravitation. 

Beautiful  instances  of  experiment  according  to  this  method  are 
to  be  found,  as  Sir  John  Herschel  has  pointed  out,  in  the  re- 
searches by  which  Dr.  Wells  discovered  the  cause  of  dew.  If  on 
a  clear  calm  night  a  sheet  or  other  covering  be  stretched  a  foot 
or  two  above  the  earth ,  so  as  to  screen  the  ground  below  from  the 


tBTDUCnVE  METHOD.  219 

open  sky  dew  will  be  found  on  the  grass  around  the  screen  bn» 
not  beneath  it.  As  the  temperature  aud  raoistuess  of  the  air,  ana 
other  circumstances,  are  exactly  the  same,  the  open  sky  must  be 
an  indispensable  antecedent  to  dew.  The  same  experiment  is, 
indeed,  tried  for  us  by  nature,  for  if  we  make  observations  of  dew 
during  two  nights  which  differ  in  nothing  but  the  absence  of 
clouds  in  one  and  their  i^)resence  in  the  other,  we  shall  find  that 
the  clear  open  sky  is  requisite  to  the  formation  of  de*v. 

It  may  often  happen  that  we  cannot  apply  the  method  of  differ- 
ence perfectly  by  varying  only  one  circumstance  at  a  time.  Tlius 
we  cannot,  generally  speaking,  try  the  qualities  of  the  same  sub- 
stance in  the  solid  and  liquid  condition  without  any  other  change 
of  circumstances,  because  it  is  necessary  to  alter  the  temperature 
of  the  substance  in  order  to  liquefy  or  solidify  it.  The  tempera- 
ture might  thus  be  the  cause  of  what  we  attribute  to  the  liquid 
or  solid  condition.  Under  such  circumstances  we  have  to  resort 
to  what  Mr.  Mill  calls  the  joint  method  of  agreement  and  differ- 
ence, which  consists  in  a  double  application  of  the  method  of 
agreement,  first  to  a  number  of  instances  where  an  effect  is  pro- 
duced, and  secondly,  to  a  number  of  quite  different  instances  where 
tne  eiteci  ie»  xiot  produced.  It  is  clearly  to  be  understood,  however, 
that  the  negative  instances  differ  in  several  circumstances  from  the 
positive  ones ;  for  if  they  differed  only  in  one  circumstance  we 
might  apply  the  simple  method  of  difference.  Iceland  spar,  for 
instance,  has  a  curious  power  of  rendering  things  seen  through 
it  apparently  double.  This  phenomenon  called  double  refraction, 
also  belongs  to  many  other  crystals ;  and  we  might  at  once  prove 
it  to  be  due  to  crystalline  structure  could  we  obtain  nny  trans- 
parent substance  crystallized  and  uncrystallized,  but  subject  to  no 
other  alteration.  We  have,  however,  a  pretty  satisfactory  proof 
by  observing  that  uniform  transparent  uncrystallized  substances 
agree  in  not  [possessing  double  refraction,  and  that  crystalline 
substances,  on  the  other  hand,  with  certain  exceptions  which  are 
easily  explained,  agree  in  possessing  the  power  in  question. 

(3)  The  principle  of  the  Joint  Method  may  be  stated 

in  the  following  rule,  which  is  Mr.  Mill's  Third  Canon  ; 

"  If  two  or  more  instances  in  which  the  pheuomenoc 


220  METHOD. 

occurs  have  only  one  circumstance  in  common,  while 
two  or  more  instances  in  which  it  does  not  occur  have 
nothing  in  common  save  the  absence  of  that  circum- 
stance; the  circumstance  in  which  alone  the  two  sets 
of  instances  (always  or  invariably)  differ,  is  the  effect, 
or  the  cause,  or  an  indispensable  pai't  of  the  cause,  of 
the  phenomenon." 

1  have  inserted  the  words  in  parentheses,  as  without  them  the 
canon  seems  to  me  to  express  exactly  the  opposite  of  what  Mr. 
Mill  intends. 

It  may  facilitate  the  exact  comprehension  of  these  inductivo 
methods  if  I  give  the  following  symbolic  representation  of  them 
in  the  manner  adopted  by  Mr.  Mill.  Let  A,  B,  G,  D,  E,  etc, 
be  antecedents  which  may  be  variously  combined,  and  let  a,  b,  e, 
d,  e,  etc.,  be  effects  following  from  them.  If  then  we  can  coUeoi 
the  following  sets  of  antecedents  and  effects — 

Antecedents.  Consequent* 
ABC  abe 

ADB  ode 

AFO  qfg 

ASK  ahk 


we  may  apply  the  method  of  agreement,  and  little  doubt  wiD 
remain  that  A,  the  sole  invariable  antecedent,  is  the  cause  of  a. 

The  method  of  difference  is  sufficiently  represented  by— 
Antecedents.  Consequents 

ABO  abe 

BO  be 

Here  while  B  and  0  remain  perfectly  unaltered  we  find  that  the 
presence  or  absence  of  A  occasions  the  presence  or  absence  of  a. 
of  which  it  is  therefore  the  cause,  in  the  presence  of  B  and  0. 
But  the  rea<ler  may  be  cautioned  a^inst  thinking:  tliat  this  provoi 
il  to  be  the  cause  of  a  under  all  circumstances  whatever. 


INDUCTIVE  METHOD.  221 

The  joint  method  of  agreement  and  difference  is  similarly 
fepreseuted  by — 

Antecedents.  Consequents. 
ABG  abe 

ADB  ode 

AF&  afg 

AHK  ahk 

PQ  "in 

B8  n 

TV  t9 

XT  wg 

Here  the  presence  of  4  is  followed  as  in  the  simple  method  of 
agreement  by  a ;  and  the  absence  of  ^4,  in  circumstances  diflFer 
ing  from  the  previous  ones,  is  followed  by  the  absence  of  a. 
Hence  there  is  a  very  high  probability  that  A  is  the  cause  of  cu 
But  it  will  easily  be  seen  that  A  is  not  the  only  circumstance  in 
which  the  two  sets  of  instances  differ,  otherwise  to  any  pair  we 
might  apply  the  simple  method  of  difference.  But  the  presence 
of  .4  is  a  circumstance  in  which  one  set  invariably,  or  uniformly, 
or  always,  differs,  from  the  other  set.  This  joint  method  is  thus 
a  substitute  for  the  simpler  method  of  difference  in  cases  where 
that  cannot  be  properly  brought  into  action. 

(4)  As  soon  as  phenomena  can  be  measured  we  can 
apply  a  further  method  of  induction  of  a  very  important 
character.  It  is  the  method  of  difference  indeed  applied 
under  far  more  favorable  circumstances,  where  every 
degree  and  quantity  of  a  phenomenon  gives  us  a  nevr 
experiment  and  proof  of  connection  between  cause  and 
effect.  It  may  be  called  the  Method  of  Concomitant 
Variations,  and  is  thus  stated  by  Mr.  Mill,  in  what  he 
entitles  the  Fifth  Canon  of  Induction  : 

"  Whatever  phenomenon  varies  in  any  manner  ry'hen* 


222  METHOD. 

ever  another  phenomenon  varies  in  some  particulai 
manner,  is  either  a  cause  or  an  effect  of  that  phe- 
nomenon, or  is  connected  with  it  through  some  fact 
of  causation." 

Sir  John  Herschel's  statement  of  the  same  method  ia 
as  follows : — "  Increase  or  diminution  of  the  effect,  with 
the  increased  or  diminished  intensity  of  the  cause,  in 
cases  which  admit  of  increase  and  diminution,"  to 
which  he  adds,  ''Eeversal  of  the  effect  with  that  of 
the  cause." 

The  illustrations  of  this  method  are  infinitely  numer- 
ous. Thus  Mr.  Joule,  of  Manchester,  conclusively 
proved  that  friction  is  a  cause  of  heat  by  expending 
exact  quantities  of  force  in  rubbing  one  substance 
against  another,  and  showed  that  the  heat  produced 
was  exactly  greater  or  less  in  proportion  as  the  force 
was  greater  or  less.  We  can  apply  the  method  to  many 
cases  which  had  previously  been  treated  by  the  simple 
method  of  difference;  thus  instead  of  striking  a  bell  in 
a  complete  vacuum  we  can  strike  it  with  a  very  little 
air  in  the  receiver  of  the  air-pump,  and  we  then  hear  a 
very  faint  sound,  which  increases  or  decreases  every 
time  we  increase  or  decrease  the  density  of  the  air. 
This  experiment  conclusively  satisfies  any  person  that 
air  is  the  cause  of  the  transmission  of  sound. 

It  is  this  method  which  often  enables  us  to  detect  the 
material  connection  which  exists  between  two  bodies. 
For  a  long  time  it  had  been  doubtful  whether  the  red 
flames  seen  in  total  eclipses  of  the  sun  belonged  to  the 
sun  or  the  moon  ;  but  during  the  hist  eclipse  of  the 
sun  it  was  noticed  that  the  flames  moved  with  the  sun, 
and  were  gradually  covered  and  uncovered  by  the  moon 


rTTDUCnVE  METHOD.  223 

at  successive  instants  of  the  eclipse.     No  one  could 
doubt  tlienceforth  that  tliey  belonged  to  the  sun. 

Whenever,  again,  phenomena  go  tlirougli  Periodic  Changes, 
alternately  increasing  and  decreasing,  we  should  seek  for  other 
phenomena  which  go  through  changes  in  exactly  the  same 
periods,  and  there  will  {)robably  be  a  connection  of  cause  and 
effect.  It  is  thus  that  the  tides  are  proved  to  be  due  to  the  at- 
traction of  the  moon  and  sun,  because  the  periods  of  higli  and 
low,  spring  and  neap  tides,  succeed  each  other  in  intervals  cor- 
responding to  the  apparent  revolutions  of  those  bodies  round  the 
earth.  The  fact  that  the  moon  revolves  upon  its  own  axis  in 
exactly  the  same  period  that  it  revolves  round  the  earth,  so  that 
for  unknown  ages  past  the  same  side  of  the  moon  has  always 
been  turned  towards  the  earth,  is  a  most  perfect  case  of  concomi- 
tant variations,  conclusively  proving  that  the  earth's  attraction 
governs  the  motions  of  the  moon  on  its  own  axis. 

The  most  extraordinary  case  of  variations,  however,  consists  in 
the  connection  which  has  of  late  years  been  shown  to  exist  be- 
tween the  Aurora  Borealis,  magnetic  storms,  and  the  spots  on  the 
8im.  It  has  only  in  the  last  30  or  40  years  become  known  that 
the  magnetic  compass  needle  is  subject  at  intervals  to  very  slight 
but  curious  movements ;  and  at  the  same  time  there  are  usually 
natural  currents  of  electricity  produced  in  telegraph  wires  so  as 
to  interfere  with  the  transmission  of  messages.  Tliese  disturb- 
ances are  known  as  magnetic  storms,  and  are  often  observed  to 
occur  when  a  fine  display  of  the  Northern  or  Southern  Lights  is 
taking  place  in  some  part  of  the  earth.  Observations  during 
many  years  have  showm  that  these  storms  come  to  their  worst  at 
the  end  of  every  eleven  years,  the  maximum  taking  place  about 
the  present  year,  1870,  and  then  diminish  in  intensity  until  the 
next  period  of  eleven  years  has  passed.  Close  observations  of 
the  sun  during  30  or  40  years  have  shown  that  the  size  and  num- 
ber of  the  dark  spots,  which  are  gigantic  storms  going  on  upon 
the  sun's  surface,  increase  and  decrease  exactly  at  the  sama 
periods  of  time  as  the  magnetic  storms  upon  the  earth's  surface. 
No  one  can  doubt,  then,  that  these  strange  phenomena  are  con 
Uected  together,  though  the  mode  of  the  connection  is  quite  im 


224  KETHOD. 

known.  It  is  now  believed  that  the  planets  Jupiter,  Saturn 
Venus  and  Mars,  are  the  real  causes  of  the  disturbances;  for  Bal- 
four Stewart  and  Warren  de  la  Rue  have  shown  that  an  exact 
correspondence  exists  between  the  motions  of  these  planets  and 
the  periods  of  the  sun-spots.  This  is  a  most  remarkable  and 
extensive  case  of  concomitant  variations. 

(5)  We  have  now  to  consider  a  method  of  induction 
which  must  be  employed  when  several  causes  act  at 
once  and  their  effects  are  all  blended  together,  pro- 
ducing a  joint  effect  of  the  same  kind  as  the  separate 
effects.  If  in  one  experiment  friction,  combustion, 
compression  and  electric  action  are  all  going  on  at  once, 
each  of  these  causes  will  produce  quantities  of  heat 
which  will  be  added  together,  and  it  will  be  diflficnlt  or 
impossible  to  say  how  much  is  due  to  each  cause 
separately.  We  may  call  this  a  case  of  tlie  homogeneous 
intermixture  of  effects,  the  name  indicating  that  the 
joint  effect  is  of  the  same  kind  as  the  separate  effects. 
It  is  distinguished  by  Mr.  Mill  from  cases  of  the  hetero- 
geneous, or,  as  he  says,  the  heteropathic  intermixture 
of  effects,  where  the  joint  effect  is  totally  different  in 
kind  from  the  separate  effects.  Thus  if  we  bend  a  bow 
too  much  it  breaks  instead  of  bending  further ;  if  we 
Tarm  ice  it  soon  ceases  to  rise  in  temperature  and 
melts ;  if  we  warm  water  it  rises  in  temperature  homo- 
geneously for  a  time  but  then  suddenly  ceases,  and  an 
effect  of  a  totally  different  kind,  the  production  of 
vapor,  or  possibly  an  explosion,  follows. 

Now  when  the  joint  effect  is  of  a  heterogeneous  kind 
the  method  of  difference  is  suflBcient  to  ascertain  the 
cause  of  its  occurrence.  Whether  a  bow  or  a  spring 
Wrill  break  with  a  given  weight  may  easily  be  tried,  and 


INDUCTIVE  METHOD.  225 

whether  water  will  boil  at  a  given  temperature  in  any 
given  state  of  the  barometer  may  also  be  easily  ascer- 
tained. But  in  the  homogeneous  intermixture  of  eflfecta 
we  have  a  more  complicated  task.  There  are  several 
causes  each  producing  a  part  of  the  effect,  and  we  want 
to  know  how  much  is  due  to  each.  In  this  case  we 
must  employ  a  further  inductive  method,  called  by  Mi. 
Mill  the  Method  of  Residues,  and  thus  stated  in  his 
Fourth  Canon  : — 

"Subduct  from  any  phenomenon  such  part  as  is 
known  by  previous  inductions  to  be  the  effect  of  cer- 
tain antecedents,  and  the  residue  of  the  phenomenon  is 
the  effect  of  the  remaining  antecedents." 

If  we  know  that  the  joint  effect  a,  b,  c  is  due  to  the 
causes  A,  B,  and  C,  and  can  prove  that  a  is  due  to  A 
and  b  to  B,  it  follows  that  c  must  be  due  to  C.  There 
cannot  be  a  simpler  case  of  this  than  ascertaining  the 
exact  weight  of  any  commodity  in  a  cart  by  weighing 
the  cart  and  load,  and  then  subtracting  the  tare  or 
weight  of  the  cart  alone,  which  had  been  previously 
ascertained.  "We  can  thus  too  ascertain  how  much  of 
the  spring  tides  is  due  to  the  attraction  of  the  sun,  pro- 
vided we  have  previously  determined  the  height  of  the 
tide  due  to  the  moon,  which  will  be  about  the  average 
height  of  the  tides  during  the  whole  lunar  month. 
Then  subtracting  the  moon's  tide  the  remamder  is  the 
sun's  tide. 

Newton  employed  this  mettod  in  a  beautiful  experiment  to 
determine  the  elasticity  of  substances  by  allowing  balls  made  of 
the  substances  to  swing  against  each  other,  and  then  observing 
how  far  they  rebounded  compared  with  their  original  fall.  But 
the  loss  of  motion  is  due  partly  to  imperfect  elasticity  and  partlj 


226  METHOD. 

to  the  resistance  of  the  air.  He  determined  the  amount  of  th« 
latter  effect  in  the  simplest  manner  by  allowing  the  balls  to 
twing  without  striking  each  other,  and  observing  how  much  each 
ribratiou  was  less  than  the  last.  In  this  waj  he  was  enabled 
easily  to  calculate  the  quantity  that  must  be  subtracted  for  the 
resistance  of  the  air. 

It  is  this  method  that  we  employ  in  making  allowance  for  th« 
errors  or  necessary  corrections  in  observations.  Few  ther- 
mometers are  quite  correct;  but  if  we  put  a  thermometer  into 
melting  snow,  which  has  exactly  the  temperature  of  0^  Centi- 
grade, or  32"  Fahr.,  we  can  observe  exactly  how  much  below  or 
above  the  true  point  the  mercury  stands,  and  this  will  indicate 
how  much  we  ought  to  add  or  subtract  from  readings  of  the 
Thermometer  to  make  them  correct.  The  height  of  the  barometer 
is  affected  by  several  causes  besides  the  variation  of  the  pressure 
of  the  air.  It  is  decreased  by  the  capillary  repulsion  between 
the  glass  tube  and  the  mercury ;  it  is  increased  by  the  expansion 
of  the  mercury  by  heat,  if  the  temperature  be  above  82°  Fahr. ; 
and  it  may  be  increased  or  decreased  by  any  error  in  the  length 
of  the  mmisure  employed  to  determine  the  height.  In  an  accurate 
observation  all  these  effects  are  calculated  and  allowed  for  in  the 
Snal  result. 

In  all  sciences  which  allow  of  measurement  of  quantities  this 
method  is  employed,  but  more  especially  in  astronomy,  the  most 
exact  of  all  the  sciences.  Almost  all  the  causes  and  effects  in  as- 
tronomy have  been  found  out  as  residual  phenomena,  that  is,  by 
calculating  the  effects  of  all  known  attractions  upon  a  planet  or 
satellite,  and  then  observing  how  far  it  is  from  the  place  thus  pie- 
dieted.  When  this  was  very  carefully  done  in  the  case  of  Uranus, 
it  was  still  found  that  the  planet  was  sometimes  before  and  some- 
times behind  its  true  place.  This  residual  effect  pointed  to  the 
jxistence  of  some  cause  of  attraction  not  then  known,  but  which 
was  in  consequence  soon  discovered  in  tlie  shape  of  the  planet 
Neptune.  The  motions  of  several  comets  have  in  this  way  been 
calculated,  but  it  is  observed  that  they  return  each  time  a  little 
Ater  than  they  ought.  This  retardation  points  to  the  existence 
of  some  obstructive  power  in  the  space  passed  through,  the 
oature  of  which  is  not  yet  understood. 


DEDUCTIVE    METHOD.  22? 

The  Btudent  is  strongly  recommended  to  read  Sir  J.  Herechel's 
Preliminary  Discourse  on  the  Study  of  Natural  Philos'/phy 
(Lardner's  Cabijiet  Cyclopcedia),  e8i)ecially  Part  II,  CLiaps.  4 
to  7,  concerning  Observation,  Experiment,  and  the  Inductive 
Processes  generally ;  Mill's  /System  of  Logic,  Book  III,  Chaps. 
8, 10, 13  and  14. 

In  this  section,  on  "luductive   Method,'*  we 
have  considered: — 

1,  The  Search  for  Facts, 

a.  The  Mule  for  Observation, 

3.  The  Uses  of  Hypotliesis  and  Theory 

4.  Dejinitions   of   Terms    Employed  in  Investi' 

gation, 
a.  Canons  of  Induction,  including : 

(1)  The  Method  of  Agreement, 

(2)  The  Method  of  Difference, 

(3)  The  Joint  Method, 

(4)  The  Method  of  Concomitant  Variations, 

(5)  Tfie  Method  of  Residues, 


SBCTIOXT    11. 

DEDUCTIVE    METHOD. 
1.  The  Predlcables. 

There  are  certain  logical  terms  known  as  predlcables. 
meaning  the  kinds  of  terms  or  attributes  which  ma}? 
always  be  predicated  of  any  subject.  Inasmuch  as  all 
truth  known  to  man  may  be  stated  in  the  form  of  a 
proposition,  it  is  important  to  know  what  these  predi- 
cables  are.  They  are  five  in  number:  genus,  species, 
difference,  property,  and  accident ;   and  when  properh 


228  METHOD. 

employed  are  of  exceeding  use  aud  importance  in  logical 
science.  It  would  neither  be  possible  nor  desirable  in 
this  work  to  attempt  to  give  any  idea  of  the  various- 
and  subtle  meanings  which  have  been  attributed  to  the 
predicables  by  ancient  writers,  and  the  most  simple  and 
useful  view  of  the  subject  is  what  alone  can  be  given 
here. 

(1)  Any  class  of  things  may  be  called  a  genus  (Greek 
yevog,  race  or  kind),  if  it  be  regarded  as  made  up  of 
two  or  more  species.  ''Element"  is  a  genus  when  we 
consider  it  as  divided  into  the  two  species  "metallic 
and  non-metallic."  Triangle  is  a  genus  as  regards  the 
species  acute-angled,  right-angled,  and  obtuse-angled, 

(2)  On  the  other  hand,  a  species  is  any  class  which 
is  regarded  as  forming  part  of  the  next  larger  class,  so 
that  the  terms  genus  and  species  are  relative  to  each 
other,  the  genus  being  the  larger  class  which  is  divided, 
and  the  species  the  two  or  more  smaller  classes  into 
which  the  genus  is  divided. 

(3)  The  difference  may  be  defined  as  the  quality  or 
sum  of  qualities  which  mark  out  one  part  of  a  genus 
from  the  other  part  or  parts.  The  difference  (Latin 
differentia,  Greek  diacpopd)  cannot  have  any  meaning 
except  in  intension  ;  and  when  we  use  all  the  terms 
wholly  in  intension  we  may  say  that  the  difference  added 
to  the  genus  makes  the  species.  Thus,  if  "  building"  be 
the  genus,  and  we  add  the  difference  "  used  for  a  dwell- 
ing," we  get  the  species  "  house."  If  we  take  "  triangle  " 
as  the  genus,  it  means  the  sum  of  the  qualities  of 
"three-sided  rectilineal  figure;"  if  we  add  the  quality 
of  "having  two  sides  equal,"  we  obtain  the  species 
"  isosceles  triangle." 


DEDUCTIVE   METHOD.  229 

It  is  indispensable,  however,  to  regard  these  expressions  in 
the  double  meaning  of  extension  and  intension.  From  the  ex. 
planatiuu  of  tliese  different  meanings  in  a  previous  chapter  it 
.  will  be  apparent  that  the  extent  of  a  genus  or  species  is  simplj 
the  number  of  individuals  included  in  it,  and  there  will  always 
be  fewer  individuals  in  the  species  than  in  tlie  genus.  In  extent 
the  genus  book  includes  all  books  of  whatever  size,  language,  or 
contents ;  if  divided  in  respect  to  size  the  species  of  book  are  folio, 
quarto,  octavo,  duodecimo,  etc  ;  and,  of  course,  each  of  these  species 
contains  much  fewer  individual  books  thau  the  whole  genus. 

In  intension  the  genus  means,  not  the  individual  things  con- 
tainec^  in  it,  but  the  sum  of  the  qualities  common  to  all  those 
things,  and  sufficient  to  mark  them  out  clearly  from  other  classes. 
The  species  similarly  means  the  sum  of  the  qualities  common  to 
all  the  individuals  forming  part  of  the  genus,  and  sufficient  to 
mark  them  out  from  the  rest  of  the  genus,  as  well  as  from  all  other 
things.  It  is  evident,  therefore,  that  there  must  be  more  qualities 
implied  in  the  meaning  of  the  species  than  of  the  genus,  for  the 
species  must  contain  all  the  qualities  of  tlie  genus,  as  well  as  a 
certain  additional  quality  or  qualities  by  which  the  several 
species  are  distinguished  from  each  other.  Now  these  additional 
qualities  form  the  difference. 

It  will  easily  be  seen  that  the  same  class  of  things  may  be 
both  a  genus  and  a  species  at  the  same  time,  according  as  we  re- 
gard it  as  divided  into  smal'er  classes  or  forming  part  of  a  larger 
class.  Thus  triangle,  which  is  a  genus  as  regards  isosceles 
triangle,  is  a  species  as  regards  right-lined  geometrical  figures. 
House  is  a  species  of  building,  but  a  genus  with  respect  to  man- 
sion, cottage,  villa,  or  other  kinds  of  houses.  We  may,  in  fact, 
have  an  almost  interminable  chain  of  genera  and  species,  each  class 
being  a  species  of  the^ass  next  above  it,  and  a  genus  as  regards 
that  next  below.  Thus  the  genus  British  subject  has  the  species 
Born  in  the  United  Kingdom,  Colonial-born,  and  Naturalized. 
Each  of  these  becomes  a  genus  as  regards  the  species  male  and 
female ;  each  species  again  may  be  divided  into  adult  and  minor, 
educated,  uneducated,  employed  in  some  occupation  or  unem- 
ployed, self-maintaining,  maintained  by  friends,  or  pauper  ;  and 
«o  on.     The  subdivision  may  thus  proceed  until  we  reach  a  class 


230  METHOD. 

of  so  restricted  extent,  that  it  cannot  be  divided  except  into 
individuals  ;  in  tliis  case  the  species  is  called  the  lowest  species 
or  inflma  species.  All  the  intermediate  genera  and  species  of 
the  chain  are  called  subaltern  (Latin  sub,  under,  and  alter,  the 
other  of  two),  because  they  stand  one  under  the  other.  If  there 
is  a  genus  which  is  not  regarded  as  a  species,  that  is,  as  part  of 
any  higher  genus,  it  is  called  the  summum  genus,  the  highest 
genus,  or  genu^  generalissimum,  the  most  general  genus.  It  is 
questionable  whether  we  can  thus  set  any  limit  to  the  chain  of 
classes.  The  class  British  subject  is  certainly  not  an  absolute 
summum  genus,  since  it  is  but  a  species  of  7>ian,  which  is  a 
species  of  animal,  living  being,  inhabitant  of  the  earth,  sub- 
stance, and  so  on.  If  there  were  any  real  summum  genus  it 
would  probably  be  "Being,"  or  "Thinly,"  or  "Object  conceiv- 
able ; "  but  we  may  usefully  employ  the  term  to  signify  the 
highest  class  of  things  comprehended  in  any  science  or  classifica- 
tion. Thus  '•  material  substance  "  is  the  summum  genus  examined 
jn  the  science  of  chemistry  ;  "  inhabitant  of  the  United  King- 
dom "  is  the  summum  genus  enumerated  and  classified  in  the 
British  census.  Logical  terras  are  only  a  species  of  words  or 
phrases,  but  they  are  the  summum  genus  as  regards  logic,  which 
has  nothing  to  do  witii  the  various  parts  of  speech  and  the  rela,- 
tions  of  words,  syllables,  ami  letters,  examined  by  grammarians. 

Several  very  useful  expressions  have  been  derived  from  the 
words  genus  and  species.  When  a  thing  is  so  peculiar  and  un- 
like other  things  that  it  cannot  easily  be  brought  into  one  class 
with  them,  it  is  said  to  be  sui  generis,  or  of  its  own  genus;  thus 
the  rings  of  Saturn  are  so  diflFerent  from  anything  else  among 
the  heavenly  bodies  that  they  may  fairly  be  called  sui  generis. 
In  zoology,  the  Omithorhynchus,  or  Australian  Duck-bill,  the 
Amphioxns,  and  some  other  animals,  aro^ro  peculiar  that  they 
may  be  called  sui  generis.  When  a  sulwtance  is  the  same  in  all 
its  parts,  or  when  a  number  of  things  are  all  alike,  we  say  that 
they  are  homi>gerwous  (Greek  i/zaclike,  yivo^,  kind),  that  is,  of  the 
same  nature  ;  otherwise  they  may  be  called  heterogeneous  (Greek 
trepo^,  other). 

It  is  npcessiiry  to  distinguish  carefully  the  purely  logical  use  of 
the  terms  genus  and  species  from  their  peculiar  use  in  natural 


DEDUCTIVE    METHOD.  231 

history.  A  species  is  there  a  class  of  plants  and  animals  sup 
posed  to  have  descended  from  common  parents,  and  to  be  the 
narrowest  class  jxjssessing  a  fixed  form  ;  the  genus  is  the  next 
higher  class.  But  if  we  accept  Darwin's  theory  of  the  origin  o! 
species,  this  definition  of  species  becomes  entirely  illusory,  since 
different  genera  and  species  must  have  according  to  this  theory 
descended  from  common  parents.  The  species  then  denotes  a 
merely  arbitrary  amount  of  resemblance  which  naturalists  choose 
to  fix  upon,  and  which  it  is  not  possible  to  define  more  exactly. 
This  use  of  the  term,  then,  has  no  connection  whatever  with  the 
logical  use,  according  to  which  any  class  of  things  whatever  is  a 
species,  provided  it  is  regarded  as  part  of  a  wider  class  or  genus. 

(4)  The  fourth  of  the  Predicables  is  Property  (Latin 
proprium,  Greek  Idiov,  own),  which  it  is  hardly  possible 
to  define  in  a  manner  free  from  objection  and  difficulty, 
but  which  may  perhaps  be  best  described  as  any  quality 
which  is  common  to  the  whole  of  a  class,  but  is  not 
necessary  to  mark  out  that  class  from  other  classes. 
Thus  it  is  a  property  of  the  genus  "  triangle"  to  have 
the  three  internal  angles  equal  to  two  right  angles ;  this 
is  a  very  remarkable  circumstance,  which  is  always 
true  of  triangles,  but  it  is  not  made  a  part  of  the  genus, 
or  is  not  employed  in  defining  a  triangle,  because  the 
possession  of  three  straight  sides  is  a  sufficient  mark. 
The  properties  of  geometncal  figures  are  very  numer- 
ous ;  the  Second  Book  of  Euclid  is  occupied  in  proving 
a  few  properties  of  rectangles;  the  Third  Book  simi- 
larly of  circles.  As  we  commonly  use  the  term  property 
it  may  or  may  not  belong  to  other  objects  as  well  as 
those  in  question :  some  of  the  properties  of  the  circle 
may  belong  also*  to  the  ellipse ;  some  of  the  properties 
of  man,  as  for  instance  the  power  of  memory,  or  o/ 
anger,  may  belong  to  other  animals. 


232  METHOD. 

Logicians  have  invented  various  subtle  divisions  of  pro- 
perties,  but  it  will  be  sufficient  to  say  that  a  peculiar  property  ia 
one  which  belongs  to  the  whole  of  a  class,  and  to  that  class  only, 
as  laughter  is  supposed  to  belong  only  to  mankind ;  the  property 
of  containing  the  greatest  space  in  a  line  of  given  length  is  pecu- 
liar to  circles.  When  a  property  is  not  peculiar,  it  may  belong  to 
other  classes  of  objects  as  well  as  that  of  which  it  is  called  the 
property.  We  may  f urtlier  distinguish  the  Generic  Property,  or 
that  which  belongs  to  the  whole  of  the  genus,  from  tlie  Specific 
Property,  which  belongs  to  the  whole  of  a  lowest  species. 

(5)  Lastly,  an  accident  (Latin  accidens,  Greek  ovuOf- 
(iTjKog)  is  any  quality  wliich  may  indifferently  belong  or 
not  belong  to  a  class,  as  the  case  may  be,  without 
affecting  the  other  qualities  of  the  class.  The  word 
means  that  which  falls  or  happens  by  cbance,  and  has 
no  necessary  connection  with  the  nature  of  a  tbing. 
Thus  the  absolute  size  of  a  triangle  is  a  pure  accident  us 
regards  its  geometrical  properties;  for  whether  the  side 
of  a  triangle  be  ^  of  an  inch  or  a  million  miles,  what- 
ever Euclid  proves  to  be  true  of  one  is  true  of  the  other. 
The  birthplace  of  a  roan  is  an  accident  concerning  him, 
as  are  also  the  clothes  in  which  he  is  dressed,  the  posi- 
tion in  which  he  rests,  and  so  on.  Some  writers  dis- 
tinguish separable  and  inseparable  accidents.  Thus 
the  clothes  in  which  a  man  is  dressed  is  a  separable 
•ccident,  because  they  can  be  changed,  as  can  also  his 
position,  and  many  other  circumstances;  but  his  birth- 
place, his  height,  his  Christian  name,  etc.,  arc  insepa- 
rable accidents,  because  they  can  never  he  changed, 
although  they  have  no  necessary  or  important  relation 
to  his  general  character. 

As  an  illaatration  of  some  part  of  the  scheme  of  classification 
described  under  the  name  of  Prodicables,  I  may  here  give,  as  ii 
osoal  in  manuals  of  Logpc,  the  Tree  of  Porphyry,  a  sort  of  ex- 


DEDUCTIVE   METHOD. 


233 


ample  of  classification  invented  by  one  of  the  earliest  Greek 
logicians,  named  Porphyrius.  I  have  simplified  the  common 
form  in  which  it  is  given  by  translating  the  Latin  names  and 
omitting  superfluous  words. 

In  this  Tree  we  observe  a  succession  of  genera  and  species — 
—Substance,  Body,  Living  Being,  Animal  and  Man.  Of  these, 
Substance  is  the  aummum  genus,  because  it  is  not  regarded  as  a 
species  of  any  higher  class ;  Man  is  the  infima  species,  because 
it  is  a  class  not  divided  into  any  lower  class,  but  only  into 
individuals,  of  whom  it  is  usual  to  specify  Socrates  and  Plato. 

Substance, 


Corporeal, 


Incorporeal, 


Body, 


Animate, 


Inanimate, 


Living  Beingf, 
I  Sensible,  Insensible. 


Animal, 


Rational, 


Irrational, 


Man, 


Socrates,  Plato,  and  others. 

Body,  Living  Being,  and  Animal  are  called  subaltern  genera 


234  METHOD. 

and  species,  because  each  is  a  species  as  regards  the  next  highei 
genus,  and  a  genus  as  regards  the  uext  lower  species.  Tiie 
qualities  implied  in  the  adjectives  Corporeal,  Animate,  Sensible 
[i.e.  capable  of  feeling)  and  Rational  are  the  successive  differences 
which  occasion  a  division  of  eacii  genus  into  species.  It  will 
be  evident  that  the  negative  parts  of  tlie  genera,  namely  Incor- 
poreal Substance,  Inanimate  Body,  etc.,  are  capable  of  sub- 
division, which  has  not  been  carried  out  in  order  to  avoid 
confusing  the  figure. 

2.  Logical  Division. 

Logical  division  is  the  name  of  the  process  by  which 
we  distinguish  the  species  of  which  a  genus  is  composed. 
Thus  we  are  said  to  divide  tiie  genus  "book"  when 
we  consider  it  as  made  up  of  the  groups  folio,  quarto, 
octavo,  duodecimo  books,  etc.,  and  the  size  of  the  books 
is  in  this  case  the  ground,  basis,  or  principle  of  divi- 
sion, commonly  called  the  Fundamentum  Divisionis.  In 
order  that  a  quality  or  circumstance  may  be  taken  as 
the  basis  of  division,  it  must  be  present  with  some  and 
absent  with  others,  or  must  vary  with  the  different 
species  comprehended  in  the  genus.  A  generic  property 
of  course,  being  present  in  the  whole  of  the  genus,  can- 
not serve  for  the  purpose  of  division.  Three  rules  may 
be  laid  down  to  which  a  sound  and  useful  division  must 
conform : 

1.  The  constituent  species  must  exclude  each  other. 

2.  The  constituent  species  must  be  equal  when  added 
together  to  the  genus. 

3.  The  division  must  be  founded  upon  one  principle 
or  ba.sis. 

It  would  be  obviously  absurd  to  divide  books  into  folio,  quarto, 
French,  German  and  dictionaries,  because  these  species  overlap 
each  other,  and  there  may  be  French  or  Oennan  dictionaries 
which  happen  to  be  quarto  or  folio  and  belong  to  three  different 


DEDUCTIVE  METHOD.  235 

species  at  ouce.  A  division  of  this  kind  is  said  to  be  a  Cross 
Division,  because  there  is  more  than  one  principle  of  division, 
and  the  several  species  in  consequence  cross  each  otlier  and  pro- 
duce confusion.  If  I  were  to  divide  rectilineal  figures  into  tri- 
angles, parallelojf ranis,  rectangles  and  polygons  of  more  than 
four  sides,  I  should  commit  all  the  possible  faults  in  onu  division. 
The  species  parallelogram  and  rectangle  do  not  exclude  each 
other,  since  all  rectangles  must  be  parallelograms ;  the  con- 
stituent species  are  not  altogether  equal  to  the  genus  rectilineal 
figure,  since  irregular  four  sided  figures  which  are  not  parallelo- 
grams have  been  omitted ;  and  there  are  three  principles  of  divi- 
sion, namely  the  number  of  sides,  the  directions  of  those  sides^ 
and  the  angles  contained.  But  when  subdivision  is  employed, 
and  each  of  the  species  is  considered  as  a  genus  which  may  be 
subjected  to  a  further  separation,  a  new  principle  of  division  may 
and  in  fact  must  be  employed  each  time.  Thus  I  can  divide 
rectilineal  figures  according  to  the  three  principles  mentioned 
above: 

Rectilineal  Figure 

8  sides  4  sides  more  than  4  sides 

Triangle  Quadrilateral  Polygon 


with  parallel  sides  without  parallel 

Parallelogram  sides 

Trapezium. 

Here  the  principles  of  division  are  the  number  of  their  sides, 
and  in  the  case  of  four-sided  figures  their  parallelism.  Triangles 
do  not  admit  of  division  in  this  second  respect.  We  may  make  a 
new  division  of  parallelograms,  adopting  the  equality  of  sides 
and  the  size  of  the  angles  as  the  principles ;  thus : 
Parallelogram 


adjoining  sides  adjoining  sides 

equal  not  equal 


I                                I  '  I.  . 

right-  not  right-  right-  not  nght 

angled  angled  angled  angled 

Square  Rlu)mbiis  Oblong  Rhomboid 


236  METHOD. 

3.  Dichotomy,  or  Exhaustive  Division. 

The  most  perfect  divisions  in  a  logical  point  of  view 
are  produced  by  continually  dividing  each  genus  into 
two  species  by  a  difference,  of  wiiich  an  example  has 
been  given  in  the  Tree  of  Porphyry.  This  process  is 
called  Dichotomy  (Greek  (Vixf^,  in  two;  Tejui'w,  to  cut) ; 
it  is  also  called  Exhaustive  Division  because  it  always  of 
necessity  obeys  the  second  rule,  and  provides  a  place 
for  every  possible  existing  thing.  By  a  law  of  Thought 
considered  in  a  previous  chapter,  every  thing  must 
either  have  a  quality  or  not  have  it,  so  that  it  must  fall 
'.nto  one  or  other  division  of  the  genus.  This  process 
of  exhaustive  division  has  considerable  importance,  but 
in  practice  it  is  not  by  any  means  always  necessary  or 
convenient.  It  would,  for  instance,  produce  a  need- 
l*?8sly  long  classification  if  we  divided  rectilineal  figures 
t  hus : 

Rectilineal  figure 


I  I 

3-8ided  not  S-sided 


Triangle 


4-8ided  not  4-8ided 


Quadrilateral 


5-8ided  not  5-8ided 

Pentagon  etc. 

As  we  know  beyond  all  doubt  that  every  figure  must 
have  3,  4,  5,  6,  or  more  sides,  and  no  6gure  can  belong 
to  more  than  one  group,  it  is  much  better  at  once  to 
enumerate  the  parts  as  Triangle,  Quadrilateral,  Penta- 
gon, Hexagon,  etc.  Again,  it  would  be  very  awkward 
if  we  divided  the  counties  of  England  into  Middlesex 


DEDUCTIVE   METHOD.  237 

and  not-Middlesex ;  the  latter  into  Surrey  and  not- 
Surrey  ;  the  latter,  again,  into  Kent  and  not-Kent.  Di- 
chotomy is  useless,  and  even  seems  absurd  in  these  cases, 
because  we  can  observe  the  rules  of  division  certainly  in 
a  much  briefer  division.  But  in  less  certain  branches  of 
knowledge  our  divisions  can  never  be  free  from  possible 
oversigiit  unless  they  proceed  by  dichotomy.  Thus, 
if  we  divide  the  population  of  the  world  into  three 
branches,  Aryan,  Semitic,  and  Turanian,  some  race 
might  ultimately  be  discovered  which  is  distinct  from 
any  of  these,  and  for  which  no  place  has  been  provided ; 
but  had  we  proceeded  thus — 

Man 

! 

Aryan  not- Aryan 


Semitic  not-Semitic 


Turanian  not  Turanian, 

it  18  evident  that  the  new  race  would  fall  into  the  last 
group,  which  is  neither  Aryan,  Semitic,  nor  Turanian. 
All  the  divisions  of  naturalists  are  liable  to  this  incon- 
venience. If  we  divide  Vertebrate  Animals  into  Mam- 
malia, Birds,  Reptiles,  and  Fish,  it  may  any  time 
happen  that  a  new  form  is  discovered  which  belongs  to 
none  of  these,  and  therefore  upsets  the  division. 

A  further  precaution  required  in  Division  is  not  to  proceed 
from  a  high  or  wide  genus  at  once  to  a  low  or  narrow  species,  or, 
as  the  phrase  is,  divisio  nonfaciat  saHum  (the  division  sliould  not 
make  a  leap)  The  species  should  always  be  those  of  the 
proximate  or  next  higher  genus ;  thus  it  would  obviously  be 


238  METHOD. 

Inconvenient  to  be^n  by  dividing  geometrical  figures  into  those 
which  have  parallel  sides  and  those  which  have  not ;  but  tliis 
principle  or  division  is  very  proper  wheu  applied  to  the  proximate 
genus. 

Logical  division  must  not  be  confused  with  physical  division  or 
Partition,  by  which  an  individual  object,  as  a  tree,  is  regarded  aa 
composed  of  its  separate  parts,  root,  trunk,  brandies,  leaves,  etc. 
There  is  even  a  third  and  distinct  process,  called  Metaphysical 
Division,  which  consists  in  rejfarding  a  thing  as  an  aggregate  of 
qualities  and  separating  these  in  thought;  as  when  we  discrimi- 
nate the  form,  color,  taste,  and  smell  of  an  orange. 

4.  Defiuiciou. 

Next  to  division  the  most  important  process  of  de- 
ductive method  is  Logical  Definition,  by  which  we 
determine  the  common  qualities  or  marks  of  the  objects 
belonging  to  any  given  class  of  objects.  We  must  give 
in  a  definition  the  briefest  possible  statement  of  such 
qualities  as  are  suflBcient  to  distinguish  the  class  from 
other  classes,  and  determine  its  position  in  the  general 
classification  of  conceptions.  Now  this  will  be  fulfilled 
by  regarding  the  class  as  a  species,  and  giving  the  proxi- 
mate genus  and  the  difference.  The  word  genus  is  here 
used  in  its  intensive  meaning,  and  denotes  the  qualities 
belonging  to  all  of  the  genus,  and  sufficient  to  mark 
them  out;  and  as  the  difference  marks  out  the  part  of 
the  genu.s  in  question,  we  get  a  perfect  definition  of  the 
species  desired.  But  we  should  be  careful  to  give  in  a 
definition  no  superfluous  marks;  if  these  are  accidents 
and  do  not  belong  to  the  whole,  the  definition  will  be 
improperly  narrowed,  as  if  we  were  to  define  Quadri- 
lateral Figures  as  figures  with  four  equal  sides ;  if  the 
superfluous  marks  belong  to  all  the  things  defined  they 
are  Properties,  and  have  no  effect  upon  tlie  definition 


DBDUCTIVE   METHOD.  289 

«rhatever.  Thus  if  I  define  parallelograms  as  "four- 
sided  rectilineal  figures,  with  the  opposite  sides  equal 
and  parallel,  and  the  opposite  angles  equal,"  I  have 
added  two  properties,  the  equality  of  the  opposite  sides 
and  angles  which  necessarily  follow  from  the  parallelism 
of  the  sides,  and  only  add  to  the  complexity  of  the 
definition  without  rendering  it  more  precise. 

There  are  certain  rules  usually  given  in  logical 
works  which  express  the  precautions  necessaiy  in  de- 
finition. 

1.  A  definition  should  state  the  essential  attributes 
of  the  species  defined.  So  far  as  any  exact  meaning 
can  be  given  to  the  expression  "essential  attributes," 
it  means,  as  explained  above,  the  proximate  genus  and 
difference. 

3.  A  defi7iition  nmst  not  contain  the  name  defined. 
For  the  purpose  of  the  definition  is  to  make  the  species 
known,  and  as  long  as  it  is  not  known  it  cannot  serve 
to  make  itself  known.  When  this  rule  is  not  observed, 
there  is  said  to  be  "  circulus  in  definiendo"  or  "  a  circle 
in  defining,"  because  the  definition  brings  us  round 
again  to  the  very  word  from  which  we  started.  This 
fault  will  usually  be  committed  by  using  a  word  in  the 
definition  which  is  really  a  synonym  of  the  name  de- 
fined, as  if  I  were  to  define  "  Plan  t "  as  "  an  organized 
being  possessing  vegetable  life,"  or  elements  as  simple 
substances,  vegetable  being  really  equivalent  to  plant, 
and  simple  to  elementary.  If  I  were  to  define  metals 
as  "substances  possessing  metallic  lustre,"  I  should 
either  commit  this  fault,  or  use  the  term  metallic  lustre 
in  a  sense  which  would  admit  other  substances,  and 
thus  break  the  following  rule. 


240  METHOD. 

3.  A  definition  must  be  exactly  equivalent  to  tht 
ipecies  defined,  that  is  to  say,  it  must  be  an  expression 
the  denotation  of  which  is  neither  narrower  nor  wider 
than  the  species,  so  jis  to  include  exactly  the  same  ob- 
jects. The  definition,  in  short,  must  denote  the  species, 
the  whole  species,  and  nothing  but  the  species,  and  this 
may  really  be  considered  a  description  of  what  a  defini- 
tion is. 

4.  A  definition  must  not  be  expressed  in  obscure, 
figurative,  or  ambiguous  language.  In  other  words, 
the  terms  employed  in  the  definition  must  be  all  exactly 
known,  otherwise  the  purpose  of  the  definition,  to  make 
us  acquainted  with  the  suflBcient  marks  of  the  species, 
is  obviously  defeated.  There  is  no  worse  logical  fault 
than  to  define  ignotum  per  ig7iolius,  the  unknown  by 
the  still  more  unknown.  Aristotle's  definition  of  the 
Boul  as  "  The  Entelechy,  or  first  form  cf  an  organized 
body  which  has  potential  life,"  certainly  seems  subject 
to  this  objection. 

5.  And  lastly,  A  definition  must  not  be  negative  where 
it  can  be  affirmative.  This  rule,  however,  is  often  not 
applicable,  and  is  by  no  means  always  binding. 

5.  Classification. 

The  joint  use  of  division  and  definition  is  necessary 
in  the  important  work  of  classification,  so  prominent 
in  all  scientific  investigations. 

Classification  may  perhaps  be  best  defined  as  the 
arrangement  of  things,  or  our  notions  of  them,  according 
to  their  resemblances  or  identifies.  Every  class  should 
be  so  constituted  as  to  contain  objects  exiictly  resem- 
bling each  other  in  certain  definite  qualities,  which  are 


DEDUCTIVE   METHOD.  24j 

stated  in  the  definition  of  the  class.  The  more  numer- 
ous and  extensive  the  resemblances  whicli  are  thua 
indicated  by  any  system  of  classes,  the  more  perfect  and 
useful  must  that  system  be  considered. 

A  collection  of  objects  may  generally  be  classified  in 
an  indefinite  number  of  ways.  Any  quality  which  is 
possessed  by  some  and  not  by  others  may  be  taken  as 
the  first  difference,  and  the  groups  thus  distinguished 
may  be  subdivided  in  succession  by  any  other  qualities 
taken  at  will.  Thus  a  library  of  books  might  be 
arranged,  (1)  according  to  their  size,  (2)  according  to 
the  language  in  which  they  are  written,  (3)  according 
to  the  alphabetic  order  of  their  author's  names,  (4) 
according  to  their  subjects;  and  in  various  other  ways. 
In  large  libraries  and  in  catalogues  such  modes  of 
arrangement  are  adopted  and  variously  combined. 
Each  different  arrangement  presents  some  peculiar  con- 
venience, and  that  mode  must  be  selected  which  best 
meets  the  especial  purpose  of  the  library  or  catalogue. 
The  population  of  a  kingdom,  again,  may  be  classified 
in  an  almost  endless  number  of  ways  with  regard  to 
different  purposes  or  sciences.  The  population  of  the 
United  Kingdom  may  be  divided  according  to  their 
place  of  birth,  as  English,  Welsh,  Scotch,  Irish,  colonial- 
born,  and  aliens.  The  ethnographer  would  divide  them 
into  Anglo-Saxons,  Cymri,  Gaels,  Picts,  Scandinavians, 
etc.  The  statist  arranges  them  according  to  age;  to 
condition,  as  married,  unmarried,  widowed,  etc.;  to 
state  of  body,  as  able,  incapacitated,  blind,  imbecile. 
The  political  economist  regards  the  innumerable  trades 
which  are  carried  on,  and  classifies  them  in  a  complex 
manner.  The  lawyer  again  treats  every  one  as  a  minor, 
11 


24^  METHOD. 

an  adult,  a  feme  sole,  a  feme  couverte,  a  guardian, 
ward,  trustee,  felon,  an.cl  so  on. 

The  derivation  of  the  word  class  is  somewhat  curious.  In 
ancient  Rome  it  was  tlie  practice  to  summon  the  whole  people 
together  at  certain  periods,  and  tliis  ceremony  was  known  as  a 
cldsis,  from  the  Greek  kauijic,  or  k/J/oi^,  derived  from  Ka?.eu,  to 
call  together.  Servius  Tullius  is  said  to  have  divided  the  people 
into  six  orders,  according  to  the  amount  of  tribute  they  could  pay, 
and  these  orders  were  not  unnaturally  called  the  classes  of  tlie 
people.  Hence  the  name  came  by  degrees  to  be  applied  to  any 
organized  body  of  people,  such  as  an  army  ;  thence  it  was  trans- 
ferred to  a  fleet  of  vessels  as  marshalled  in  a  fixed  order,  and  was 
finally  extended  by  analogy  to  any  collection  of  objects  carefully 
arranged.  When,  however,  we  now  speak  of  the  lower  or  higher 
classes  of  the  people  it  is  curious  that  we  are  restoring  the  word 
very  nearly  to  its  original  meaning. 

6.  Requisites  of  a  Good  Classification. 

A  good  classification  has  certain  requisites,  which 
may  be  named  as  follows : 

(1)  The  first  requisite  of  a  good  classification  is,  that 
it  shall  be  appropriate  to  the  purpose  in  hand ;  that  is 
to  say,  the  points  of  resemblance  selected  to  form  the 
leading  classes  shall  be  those  of  importance  to  the  prac- 
tical use  of  the  classification.  All  those  things  must  be 
arranged  together  wliich  require  to  be  treated  alike, 
and  those  things  must  be  separated  which  require  to  be 
treated  separately.  Thus  a  lawyer  has  no  need  to  classify 
persons  according  to  the  counties  of  England  they  were 
bom  in,  because  the  law  is  the  same  independently  of 
counties ;  but  so  far  as  a  Scotchman,  a  Manx  man,  or 
an  alien,  is  under  different  laws  from  the  English-bom 
man,  we  shall  require  to  classify  them  apart.     A  gar- 


DEDUCTIVE   METHOD.  243 

dener  is  quite  right  in  classifying  plants  as  annuals, 
biennials,  perennials;  as  herbs,  shrubs,  trees;  as  ever- 
green and  deciduous  ;  or  according  to  the  soil,  tempera- 
ture and  other  circumstances  which  affect  them,  because 
these  are  points  which  must  guide  him  in  treating 
some  differently  from  others. 

(2)  Another  and,  in  a  scientific  point  of  view,  the 
most  important  requisite  of  a  good  classification,  is 
that  it  shall  enable  the  greatest  possible  number  of 
general  assertions  to  be  made.  This  is  the  criterion, 
as  stated  by  Dr.  Whewell,  which  distinguishes  a  natural 
from  an  artificial  system  of  classification,  and  we  must 
carefully  dwell  upon  its  meaning.  It  will  be  apparent 
that  a  good  classification  is  more  than  a  mere  orderly 
arrangement ;  it  involves  a  process  of  induction  which 
will  bring  to  light  all  the  more  general  relations  which 
exist  between  the  things  classified.  An  arrangement 
of  books  will  generally  be  artificial ;  the  octavo  volumes 
will  not  have  any  common  character  except  being  of  an 
octavo  size.  An  alphabetical  arrangement  of  names 
again  is  exceedingly  appropriate  and  convenient  to  many 
purposes,  but  is  artificial  because  it  allows  of  few  or  no 
general  assertions.  We  cannot  make  any  general  asser- 
tion whatever  about  persons  because  their  names  happen 
to  begin  with  an  A  or  a  B,  a  P  or  a  W.  Even  those 
who  agree  in  bearing  the  name  Smith  or  Taylor  or 
Kobinson  might  be  submitted  to  the  inductive  method 
of  agreement  without  the  discovery  of  any  common 
circumstance  which  could  be  stated  in  a  general  propo- 
sition or  law.  It  is  true  that  if  we  investigated  the 
antecedents  of  the  Evanses  and  Joneses  we  should  find 
them  nearly  all  to  be  Welsh,  and  the  Campbells  to  be 


244  METHOD. 

Scotch,  and  those  who  bear  a  very  peculiar  name  would 
often  be  found  to  descend  from  common  ancestors.  So 
far  even  an  alphabetic  arrangement  embodies  some- 
tuing  that  is  natural  in  it,  and  enables  general  asser- 
tions to  be  made.  Hardly  any  arrangement  can  be 
made,  in  fact,  which  will  not  indicate  some  vestiges  of 
important  relations  and  resemblances  ;  but  what  we 
want  is  a  system  which  will  reveal  all  the  most  impor- 
tant general  truths. 

(3)  For  this  purpose  we  must  select  as  the  ground  of 
union  those  characters  which  carry  with  them  most  other 
characters.  We  have  considered  the  proprium  as  a 
quality  which  belongs  to  the  whole  of  a  class  without 
forming  part  of  the  definition  of  the  class.  Now  we 
ought  to  frame  the  definition  of  a  class  that  it  may  con- 
tain as  few  characters  as  possible,  but  that  as  many 
other  characters,  properties,  or  propria,  as  possible, 
shall  be  attributable  to  the  things  contained  in  the  class. 
Every  one  can  see,  for  instance,  that  animals  form  one 
great  group  of  beings,  which  have  many  characters  in 
common,  and  that  plants  form  another  group.  Animals 
have  sensation,  voluntary  motion,  consume  carbona- 
ceous food,  and  evolve  carbonic  acid,  possess  a  stomach, 
and  produce  fat.  Plants  are  devoid  of  sensation  and 
voluntary  motion,  produce  carbonaceous  tissue,  absorb 
carbonic  acid,  and  evolve  oxygen,  possess  no  stomach, 
and  produce  starch.  At  one  time  it  might  have  been 
thought  that  almost  any  of  the  characters  named  was  a 
sufficient  mark  of  the  group  to  which  a  being  belonged. 
Whatever  had  a  stomach,  was  an  animal;  whatever 
had  not,  was  a  plant;  whatever  produced  starch  or 
evolved  oxygen  was  called  a  plant ;  whatever  absorbed 


DEDUCTIVE   METHOD.  245 

oxygen  or  produced  fat  was  an  animal.  To  the  present 
iay  these  statements  remain  generally  true,  so  that  we 
may  make  assertions  in  the  form  of  the  proposition  U, 
that  ''all  animals  are  all  beings  that  evolve  carbonic 
acid,  and  all  plants  are  all  beings  that  absorb  carbonic 
acid."  But  in  reality  the  exceptions  are  many,  and 
increasing  research  makes  it  continually  more  apparent 
that  there  is  no  definite  line  to  be  drawn  between 
animal  and  vegetable  life.  This,  of  course,  is  not  a 
failure  of  logical  science,  but  a  fact  of  great  significance 
concerning  the  things  themselves. 

7.  Denomination. 

In  order  to  employ  our  results  of  classification,  if  not 
in  the  formation  of  classes,  we  need  to  name  the  pro- 
duct of  our  labors  of  division  and  definition.  This 
process  is  Denomination. 

It  is  apparent  that  language  serves  three  distinct  and 
almost  independent  purposes  : — 

1.  As  a  means  of  communication. 

2.  As  a  mechanical  aid  to  thought. 

3.  As  an  instrument  of  record  and  reference. 

In  its  first  origin  language  was  used  chiefly  if  not 
exclusively  for  the  first  purpose.  Savage  tribes  exist  in 
great  numbers  at  the  present  day  who  seem  to  accumu- 
late no  knowledge.  We  may  even  say  that  the  lower 
animals  often  possess  some  means  of  communication  by 
sounds  or  natural  signs  which  constitute  language  in 
the  first  sense,  though  they  are  incapable  of  reasoning 
by  general  notions. 

Some  philosophers  have  held  that  it  is  impossible  to 
carry  on  reasoning  without  the  use  of  language.     The 


346  METHOD. 

true  nominalist  went  so  far  as  to  say  that  there  are  no 
such  things  as  general  notions,  and  that  general  names 
therefore  constitute  all  that  is  general  in  science  and 
reasoning.  Though  this  is  no  doubt  false,  it  must 
nevertheless  be  allowed  that  unless  general  ideas  were 
fixed  and  represented  by  words,  we  could  never  attain 
to  sustained  tliought  such  as  we  at  present  enjoy.  The 
use  of  language  in  the  second  purpose  is,  doubtless, 
indispensable  in  a  practical  point  of  view,  and  reason- 
ing may  almost  be  considered  identical  with  the  correct 
use  of  words.  When  language  is  used  solely  to  assist 
reasoning  there  is  no  need  that  the  meaning  of  each 
word  should  be  fixed;  we  might  use  names,  as  the  let- 
ters X,  y,  z,  a,  b,  c,  etc.,  are  used  in  algebra  to  denote 
any  quantity  that  happeus  to  occur  in  a  problem.  All 
that  is  requisite  is  never  to  confuse  the  meaning  attri- 
buted to  a  word  in  one  argument  with  the  different 
meaning  attributed  in  another  argument.  Algebra 
may,  in  fact,  be  said  to  consist  of  a  language  of  a  very 
perfect  kind  adapted  to  the  second  purpose  only,  and 
capable  of  leading  a  person  to  the  solution  of  a  problem 
in  a  symbolical  or  mechanical  manner. 

Language,  as  it  is  furnished  to  us  ready  made  by  the 
habitual  growth  of  centuries,  is  capable  of  fulfilling  all 
three  purposes,  though  by  no  means  in  a  perfect  man- 
ner. As  words  possess  a  more  or  less  fixed  customary 
meaning  we  can  not  only  reason  by  their  aid,  but  com- 
municate our  thoughts  or  record  them  ;  and  it  is  in 
this  last  respect  we  have  now  to  treat  the  subject. 

The  multitude  of  facts  required  for  the  establish- 
ment of  a  science  could  not  be  retained  in  the  memory; 
with  sufficient  accuracy.    Hence  an  indispensable  sub* 


DEDUCTIVE   METHOD.  24? 

sidiary  of  reasoning  is  the  means  of  describing  and  re- 
cording our  observations.  Thus  only  can  knowledge 
be  accumulated,  so  that  each  observer  shall  start  with 
the  advantage  of  knowing  what  has  been  previously 
recorded  and  proved.  It  will  be  necessary  then  to  con- 
sider the  mode  in  which  language  serves  for  the  regis- 
tration of  facts,  and  to  investigate  the  requisite  quali- 
ties of  a  philosophical  language  suitable  to  the  needs  of 
science. 

As  an  instrument  of  pecord  language  must  evidently 
possess  two  principal  requisites: 

1.  Precision  or  definiteness  of  meaning. 

2.  Completeness. 

A  name  is  Avorse  than  useless  unless,  when  used  to 
record  a  fact,  it  enables  us  to  ascertain  what  was  the 
nature  of  the  fact  recorded.  Accuracy  and  precision  is 
then  a  more  important  quality  of  language  than  abun- 
dance. The  want  of  an  appropriate  word  will  seldom 
give  rise  to  actual  error  and  fallacy;  it  will  merely 
oblige  us  to  employ  a  circumlocutory  phrase  or  else 
leave  the  fact  unrecorded.  But  it  is  a  self-evident  con- 
venience that  whenever  a  thing,  notion,  or  quality  has 
often  to  be  referred  to  there  should  be  a  name  appro- 
priate! to  the  purpose,  and  there  ought  to  be  one 
name  only. 

It  may  not  previously  have  struck  the  learner,  but  it  is  certainly 
true,  that  description  is  impossible  without  the  assertion  of 
resemblance  between  the  fact  described  and  some  other  fact. 
We  can  describe  a  thing  only  by  giving  it  a  name  ;  but  how  can 
we  learn  the  meaning  of  that  name  ?  If  we  describe  the  name 
by  other  names  we  only  have  more  names  of  which  the  meanings 
are  required.  We  must  ultimately  learn  the  meanings,  not  from 
names,  but  from  things  which  bear  those  names.    If  any  one  were 


248  METHOD. 

ignorant  of  the  meaning  of  blue  ho  could  not  be  informed  but  by 
reference  to  something  that  excited  in  him  the  sensation  of  bltie- 
ness,  and  had  he  been  blind  from  birth  he  could  not  acquire  any 
notion  of  what  blueness  is.  There  are,  indeed,  a  number  of 
words  so  familiar  to  us  from  childhood  that  we  cannot  tell  when 
or  how  we  learned  their  meanings,  though  it  must  have  been  by 
reference  to  things.  But  when  we  come  to  the  more  precise  use 
of  names  we  soon  have  to  make  fresh  reference  to  physical  ob- 
jects. Then  we  should  describe  the  several  kinds  of  blue  color 
as  sky-blue,  azure-blue,  indigo-blue,  cobalt-blue  ;  green  color  we 
likewise  distinguish  as  sea  green,  olive-jfreen,  emerald-green, 
grass  green,  etc.  The  shapes  of  leaves  are  described  in  Botany 
by  such  names  as  ovate,  lanceolate,  linear,  pinnate,  peltate,  refer- 
ring the  mind  respectively  to  an  egg,  a  lance,  a  line,  a  feather, 
and  a  shield.  In  recording  dimensions  it  is  equally  impossible 
to  avoid  comparison  with  the  dimensions  of  other  things.  A 
yard  or  a  foot  has  no  meaning  unless  there  be  a  definite  standard 
yard  or  foot  which  fixes  its  meaning;  and  the  learner  is  prob- 
ably aware  that  when  the  physical  standard  of  a  length  is  once 
completely  lost  it  can  never  be  recovered.  The  word  is  nothing 
unless  we  somewhere  have  the  thing  to  which  it  corresponds. 

See  Dr.  VVhewell's  "Aphorisms  concerning  the  Language  of 
Science."  at  the  end  of  his  Philosophy  of  the  Inductive 
Sciences. 

Thomson's  Outline  of  the  Laws  of  Thought,  contains  most 
interesting  remarks  on  the  general  nature  and  use  of  Lan- 
guage, Sections  17-3L 

In  this  section,  on  "Deductive  Metliod,"  we 
have  considered : — 

1.  The  Predicablea, 

2.  Lof/ical  Division,. 

3.  Dichotomy,  or  Exhaustive  Division. 
4t.  Definition. 

6.  Classification. 

6.  Requisites  of  a  Qitod  dassification. 

7.  Denotnination. 


OOMPLBTE   METHOD.  249 

8BGTI0IT    in. 

CO^APLETE     METHOD. 

1.  Empirical  and  Rational  Kuowledge. 

When  a  law  of  nature  is  ascertained  purely  by  in« 
ductiou  from  certain  observations  or  experiments,  and 
has  no  other  guarantee  for  its  truth,  it  is  said  to  be  an 
empirical  law.  As  Mr.  Mill  says,  "  Scientific  inquirers 
give  the  uame  of  Empirical  Laws  to  uniformities  whirf^ 
observation  or  experiment  has  shown  to  exist,  but  on 
which  they  hesitate  to  rely  in  cases  varying  much  from 
those  which  have  been  actually  observed,  for  want  of 
seeing  any  reason  why  such  a  law  should  exist."  The 
name  is  derived  from  the  Greek  word  ifmsipla,  meaning 
experience  or  trial.  Instances  of  such  laws  are  abun- 
dant. We  learn  empirically  that  a  certain  strong  yellow 
color  at  sunset,  or  an  unusual  clearness  in  the  air,  por- 
tends rain  ;  that  a  quick  pulse  indicates  fever ;  that 
horned  animals  are  always  ruminants;  that  quinine 
affects  beneficially  the  nervous  system  and  the  health  of 
the  body  generally ;  that  strychnine  has  a  terrible  effect 
of  the  opposite  nature :  all  these  are  known  to  be  true 
by  repeated  observation,  but  we  can  give  no  other  rea- 
son for  their  being  true,  that  is,  we  cannot  bring  them 
into  harmony  with  any  other  scientific  facts;  nor  could 
we  at  all  have  deduced  them  or  anticipated  them  on  the 
ground  of  previous  knowledge.  The  connection  be- 
tween the  sun's  spots,  magnetic  storms,  auroras,  and 
the  motions  of  the  planets  mentioned  in  the  last  lesson, 
is  perhaps  the  most  remarkable  known  instance  of  an 


250  METHOD. 

empirical  induction  ;  for  no  hint  has  yet  been  given  ol 
ihe  way  in  which  these  magnetic  influences  are  exerted 
throughout  the  vast  dimensions  of  the  planetary  system. 
ihe  qualities  of  the  several  alloys  of  metals  are  also 
good  instances  of  empirical  knowledge.  No  one  can 
tell  before  mixing  two  or  three  metals  for  the  first  time 
in  any  given  proportions  what  the  qualities  of  the  mix- 
ture will  be — that  brass  should  be  both  harder  and  more 
ductile  than  either  of  its  constituents,  copper  and  zinc  ; 
that  copper  alloyed  with  the  very  soft  metal  tin  should 
make  hard  and  sonorous  bell-metal ;  that  a  certain  mix- 
ture of  lead,  bismuth,  tin  and  cadmium,  should  melt 
with  a  temperature  (65°  cent.)  far  below  that  of  boiling 
water. 

However  useful  may  be  empirical  knowledge,  it  is  yet 
of  slight  importance  compared  with  the  well-connected 
and  perfectly  explained  body  of  knowledge  wiiich  con- 
stitutes an  advanced  and  deductive  science.  It  is  in 
fact  in  proportion  as  a  science  becomes  deductive,  and 
enables  us  to  grasp  more  and  more  apparently  uncon- 
nected facts  under  the  same  law,  that  it  becomes  per- 
fect. He  who  knows  exactly  why  a  thing  happens,  will 
also  know  exactly  in  what  cases  it  will  happen,  and 
what  difiference  in  the  circumstances  will  prevent  the 
event  from  happening.  Take  for  instance  the  simple 
effect  of  hot  water  in  cracking  glass.  This  is  usually 
learnt  empirically.  Most  people  have  a  confused  idea 
that  hot  water  has  a  natural  and  inevitable  tendency  to 
break  glass,  and  that  thin  glass,  being  more  fragile  than 
other  glass,  will  be  more  easily  broken  by  hot  water. 
Physical  science,  however,  gives  a  very  clear  reason  for 
the  effect,  by  showing  that  it  is  only  one  case  of  the 


COMPLETE    METHOD.  251 

general  tendency  of  heat  to  expand  substances.  The 
(Srack  is  caused  by  the  successful  effort  of  the  heated 
glass  to  expand  in  spite  of  the  colder  glass  with  which 
it  is  connected.  But  then  we  shall  see  at  once  that  the 
same  will  not  be  true  of  thin  glass  vessels ;  the  heat 
will  pass  so  quickly  through  that  the  glass  will  be  nearly 
equally  heated ;  and  accordingly  chemists  habitually 
use  thin  uniform  glass  vessels  to  hold  or  boil  hot  liquids 
without  fear  of  the  fractures  which  would  be  sure  to 
take  place  in  thick  glass  vessels  or  bottles. 

We  have  hitherto  treated  of  Deduction  and  Induction  as  if  they 
were  entirely  separate  and  independent  methods.  In  reality  they 
are  frequently  blended  or  employed  alternately  in  the  pursuit  of 
truth  ;  and  it  may  be  said  that  all  the  more  important  and  exten- 
sive investigations  of  science  rely  upon  one  as  much  as  upon  the 
other.  It  is  probably  the  greatest  merit  in  Mr.  Mill's  logical 
writings  that  he  points  out  the  entire  insufficiency  of  what  is 
called  the  Baconian  Method  to  detect  the  more  obscure  and 
difficult  laws  of  nature.  Bacon  advised  that  we  should  always 
begin  by  collecting  facts,  classifying  them  according  to  their 
agreement  and  diflFerence,  and  gradually  gathering  from  them 
laws  of  greater  and  greater  generality.  He  protested  altogether 
against  "anticipating  nature,"  that  is,  forming  our  own  hypoth- 
eses and  theories  as  to  what  the  laws  of  nature  probably  are,  and 
he  seemed  to  think  that  systematic  arrangement  of  facts  would 
take  the  place  of  all  other  methods.  The  learner  will  soon  see 
that  the  progress  of  Science  has  not  confirmed  his  opinions. 

2.  The  Elements  of  Complete  Method. 

Combined  or  Complete  Method,  consists  in  the  alter- 
nate use  of  induction  and  deduction.  It  may  be  said 
to  have  three  steps,  as  follows : — 

1.  Direct  Induction. 


253  METHOD. 

2.  Deduction,  or,  as  Mr.  Mill  calls  it,  Ratiocination. 

3.  Verification. 

The  first  process  consists  in  such  a  rough  and  simple 
appeal  to  experience  as  may  give  us  a  glimpse  of  the 
laws  which  operate,  without  being  sufficient  to  establish 
their  truth.  Assuming  them  as  provisionally  true,  we 
then  proceed  to  argue  to  their  effects  in  other  cases,  and 
a  further  appeal  to  experience  either  verifies  or  negatives 
the  truth  of  the  laws  assumed.  There  are,  in  short, 
two  appeals  to  experience  connected  by  the  intermediate 
use  of  reasoning.  Newton,  foi  instance,  having  passed  a 
ray  of  sun-light  through  a  glass  prism  found  that  it 
was  spread  out  into  a  series  of  colors  resembling  those 
of  the  rainbow.  He  adopted  the  theory  that  white 
light  was  actually  composed  of  a  mixture  of  different 
colored  lights,  which  become  separated  in  passing 
through  the  prism.  He  saw  that  if  this  were  true,  and 
he  were  to  pass  an  isolated  ray  of  the  spectrum,  for 
instance,  the  yellow  ray,  through  a  second  prism,  it 
ought  not  to  be  again  broken  up  into  diflFerent  colors, 
but  should  remain  yellow  whatever  was  afterwards  done 
with  it.  On  trial  he  found  this  to  be  the  case,  and 
afterwards  devised  a  succession  of  similar  confirmatory 
experiments  which  verified  his  theory  beyond  all  pos- 
sible doubt. 

The  greatest  result  of  the  complete  method  is  no  less  than  the 
theory  of  gravitation,  which  makes  a  perfect  instance  of  its 
procedure.  In  this  ca.se  the  preliminary  induction  consisted,  we 
may  suppose,  in  the  celebrated  fall  of  the  apple,  which  occurred 
while  Newton  was  sitting  in  an  orchard  during  his  retirement 
from  London,  on  account  of  the  Great  Plague.  The  fall  of  the 
apple,  we  are  told,  led  Newton  to  reflect  that  there  must  be  a 


COMPLETE  METHOD.  253 

power  tending  to  draw  bodies  towards  the  earth,  and  he  asked 
himself  the  question  why  the  moon  did  not  on  that  account  lall 
upon  the  earth.  The  Lancashire  astronomer  llorrocks  suggested 
to  his  mind  anotlier  fact,  namely,  that  when  a  stone  is  whirled 
round  attached  to  a  string,  it  exerts  a  force  u[)on  tlie  string,  often 
called  centrifugal  force.  Horrocks  remarked  that  tlie  planets  in 
revolving  round  the  sun  must  tend  in  a  similar  way  to  fly  ofl 
from  the  centre.  Newton  was  acquainted  with  Horrocks'  views, 
and  was  thus  possibly  led  to  suppose  that  the  earth's  attractive 
force  might  exactly  neutralize  the  moon's  centrifugal  tendency, 
so  as  to  maintain  that  satellite  in  constant  rotation. 

But  it  happened  that  the  world  was  in  possession  of  certain 
empirical  laws  concerning  the  motions  of  the  planets,  without 
which  Newton  could  scarcely  have  proceeded  further.  Kepler 
had  passed  a  lifetime  in  observing  the  heavenly  bodies,  and 
forming  hypotbeses  to  explain  their  motions.  In  general  hia 
ideas  were  wild  and  unfounded,  but  the  labors  of  a  lifetime  were 
rewarded  in  the  establishment  of  the  three  laws  which  bear  his 
name,  and  describe  the  nature  of  the  orbits  traversed  by  the 
planets,  and  the  relation  between  the  size  of  such  orbit  and  the 
time  required  by  the  planet  to  traverse  it.  Newton  was  able  to 
show  by  geometrical  reasoning  that  if  one  body  revolved  round 
another  attracted  towards  it  by  a  force  decreasing  as  the  square 
of  the  distance  increases,  it  would  necessarily  describe  an  orbit 
of  which  Kepler's  laws  would  be  true,  and  which  would  there- 
fore exactly  resemble  the  orbits  of  the  planets.  Here  was  a 
partial  verification  of  his  theory  by  appeal  to  the  results  of  ex- 
perience. But  several  other  philosophers  had  gone  so  far  in  the 
investigation  of  the  subject.  It  is  Newton's  chief  claim  to 
honor,  that  he  carried  on  his  deductions  and  verifications  until  he 
attained  complete  demonstration.  To  do  this  it  was  necessary 
first  of  all  to  show  that  the  moon  actually  does  fall  towards  tht 
earth  just  as  rapidly  as  a  stone  would  if  it  were  in  the  same  cir- 
cumstances. Using  the  best  information  then  attainable  as  to  the 
distance  of  the  moon,  Newton  calculated  that  the  moon  falls 
through  the  space  of  13  feet  in  one  minute,  but  that  a  stone,  if 
elevated  so  high,  would  fall  through  15  feet.  Most  men  would 
have  considered  this  approach  to  coincidence  as  a  proof  of  his 


254  METHOD. 

theory,  but  Newton's  love  of  certain  truth  rendered  him  different 
even  from  most  philosophers,  and  the  discrepancy  caused  him  to 
lay  "  aside  at  that  time  any  further  thoughts  of  this  matter." 

It  was  not  till  many  years  afterwards  (probably  15  or  16)  that 
Newton,  hearing  of  some  more  exact  data  from  which  he  could 
calculate  the  distance  of  the  moon,  was  able  to  explain  the  dis- 
crepancy. His  theory  of  gravitation  was  then  verified  so  far  as  the 
moon  was  concerned ;  but  this  was  to  him  only  the  beginning  of  a 
long  course  of  deductive  calculations,  each  ending  in  a  verification. 
If  the  earth  and  moon  attract  each  other,  and  also  the  sun  and  the 
earth,  similarly  there  is  no  reason  why  the  sun  and  moon  should 
not  attract  each  other.  Newton  followed  out  the  consequences 
of  this  inference,  and  showed  that  the  moon  would  not  move  as 
if  attracted  by  the  earth  only,  but  sometimes  faster  and  some- 
times slower.  Comparisons  with  Flamsteed's  observations  of  the 
moon  showed  that  such  was  the  case.  Newton  argued  again, 
that  as  the  waters  of  the  ocean  are  not  rigidly  attached  Uj  the 
earth,  they  might  attract  the  moon,  and  be  attracted  in  return, 
independently  of  the  rest  of  the  earth.  Certain  daily  motions 
would  then  be  caused  thereby  exactly  resembling  the  tides,  and 
there  were  the  tides  to  verify  the  fact.  It  was  the  almost  super- 
human power  with  which  he  traced  out  geometrically  the  conse- 
quences of  his  theory,  and  submitted  them  to  repeated  compari- 
son with  experience,  which  constitutes  his  pre-eminence  over  all 
philosophers. 

3.  The  Nature  of  Explauation. 

Explanation  is  literally  the  making  plain  or  clear,  so 
that  there  shall  be  nothing  uneven  or  obscure  to  inter- 
rupt our  view.  Scientific  explanation  consists  in  har- 
monizing fact  with  fact,  or  fact  with  law,  or  law  with 
law,  so  that  we  may  see  them  both  to  be  cases  of  one 
nniform  law  of  causation.  If  we  hear  of  a  great  earth- 
qnake  in  some  part  of  the  world,  and  subsequently  hear 
that  a  neighboring  volcano  has  broken  out,  we  say  that 
the  earthquake  is  thus  partially  explained.     The  erup- 


OOMPLBTE   METHOD.  25A 

tion  shows  that  there  were  great  forces  operating  be* 
neath  the  earth's  surface,  and  the  earthquake  is  obvi- 
ously an  effect  of  such  causes.  The  scratches  which 
may  be  plainly  seen  upon  the  surface  of  rocks  in  cer- 
tain parts  of  Wales  and  Cumberland,  are  explained  by 
the  former  existence  of  glaciers  in  those  mountains; 
the  scratches  exactly  harmonize  with  the  effects  of 
glaciers  now  existing  in  Switzerland,  Greenland,  and 
elsewhere.  These  may  be  considered  explanations  of 
fact  by  fact. 

A  fact  may  also  be  explained  by  a  general  law  of 
nature,  that  is,  the  cause  and  mode  of  its  production 
may  be  pointed  out  and  shown  to  be  the  same  as  oper- 
ates in  many  apparently  different  cases.  Thus  the 
cracking  of  glass  by  heat  may  be  explained  as  one  result 
of  the  universal  law  that  heat  increases  the  dimensions 
of  solid  bodies.  The  trade-winds  are  explained  as  one 
case  of  the  general  tendency  of  warm  air  to  rise  and  be 
displaced  by  cold  and  dense  air.  The  very  same  simple 
laws  of  heat  and  mechanics  which  cause  a  draught  to  flow 
up  a  chimney  when  there  is  a  fire  below,  cause  winds 
to  blow  from  each  hemisphere  towards  the  equator. 
At  the  same  time  the  easterly  direction  from  which  the 
winds  come  is  explained  by  the  simplest  laws  of  motion  ; 
for  as  the  earth  rotates  from  west  to  east,  and  moves 
much  more  rapidly  at  the  equator  than  nearer  the 
poles,  the  air  tends  to  preserve  its  slower  rate  of  motion, 
and  the  earth  near  the  equator  moving  under  it  occa- 
sions an  apparent  motion  of  the  wind  from  east  to 
west. 

There  are,  according  to  Mr.  Mill,  three  distinct  ways  in  which 


256  METHOD. 

one  law  may  be  explained  by  other  laws,  or  brought  Into  hxt 
mony  witli  them. 

The  first  is  the  case  where  there  are  really  two  or  more  separate 
causes  in  action,  the  results  of  which  are  combined  or  added  to- 
gether, homogeneously.  As  was  before  explained,  homogeneous 
Intermixture  of  effects  means  that  the  joint  effect  is  simply  the 
sum  of  the  separate  effects,  and  is  of  the  same  kind  with  them. 
Our  last  example  of  the  trade- winds  really  comes  under  this  case, 
for  we  find  tliat  there  is  one  law  or  tendency  which  causes  winds 
to  blow  from  the  arctic  regions  towards  the  equator,  and  a  second 
tendency  which  causes  them  to  blow  from  east  to  west.  These 
tendencies  are  combined  together,  and  cause  the  trade-winds  to 
blow  from  the  north-east  in  the  northern  hemisphere,  and  from 
the  south-east  in  the  southern  hemisphere  The  law  according 
to  which  the  temperature  of  the  air  is  governed  in  any  part  of  the 
earth  is  a  very  complicated  one,  depending  partly  on  the  law  by 
which  the  sun's  heating  power  is  governed,  partly  on  the  power 
of  the  earth  to  radiate  the  heat  away  into  space,  but  even  more 
perhaps  on  the  effect  of  currents  of  air  or  water  in  bringing 
warmth  or  carrying  it  away.  The  path  of  a  cannon  ball  or  other 
projectile  is  determined  by  the  joint  action  of  several  laws;  first, 
the  simple  law  of  motion,  by  which  any  moving  body  tends  to 
move  onward  at  a  uniform  rate  in  a  straight  line  ;  secondly,  the 
law  of  gravity,  which  continually  deflects  the  body  towards  the 
earth's  surface ;  tliirdly,  the  resistance  of  the  air,  which  tends  to 
diminish  its  velocity. 

In  the  second  case  of  explanation  an  effect  is  shown  to  be  due, 
not  to  the  supposed  cause  directly,  but  to  an  intermediate  effect 
of  that  cause.  Instead  of  A  being  the  cause  of  C,  it  is  found 
that  A  is  the  cause  of  B,  and  B  the  causn  of  <?,  so  that  B  consti- 
tutes an  intermediate  link.  This  explanation  may  seem  to  in- 
crease the  complexity  of  the  matter,  but  it  really  simplifies  it; 
for  the  connection  of  A  with  B  may  be  a  case  of  a  familiar  and 
simple  law,  and  so  may  that  of  B  with  C\  whereas  the  law  that 
A  produces  Cmay  be  purely  empirical  and  apparently  out  of  har- 
mony with  everything  else.  Thus  in  lightning  it  seems  as  it 
electricity  had  the  ])ower  of  creating  a  loud  explosion  ;  but  in 
reality  electricity  only  produces  heat,  and  it  is  the  heat  which 


COMPLETE   METHOD.  267 

occatdons  Boaad  by  suddenly  expanding  the  air.  Thus  thundet 
comes  into  harmony  with  the  sound  of  artillery,  which  is  als« 
occasioned  by  the  sudden  expansion  of  the  heated  gases  emitted 
by  the  powder.  When  chlorine  was  discovered  it  was  soon  found 
to  have  a  strong  power  of  bleaching,  and  at  the  present  day 
almost  all  bleaching  is  done  by  chlorine  instead  of  the  sun  as 
formerly.  Inquiry  showed,  however,  that  it  was  not  really  the 
chlorine  which  destroyed  color,  but  that  oxygen  is  the  inter- 
mediate and  active  agent.  Chlorine  decomposes  water,  and  tak- 
ing the  hydrogen  leaves  the  oxygen  in  a  state  of  great  activity 
and  ready  to  destroy  the  organic  coloring  matter.  Thus  a  num- 
ber of  facts  are  harmonized ;  we  learn  why  dry  chlorine  does  not 
bleach,  and  why  there  are  several  other  substances  which  re- 
semble chlorine  in  its  bleaching  power,  for  instance,  ozone, 
peroxide  of  hydrogen,  sulphurous  acid,  and  a  peculiar  oxide  of 
vanadium,  lately  discovered  by  Dr.  Roscoe,  It  would  be  impos- 
sible to  understand  the  effect  at  all  unless  we  knew  that  it  la 
probably  due  to  active  oxygen  or  ozone  in  all  the  cases,  even  in 
the  old  method  of  bleaching  by  exix)sure  to  the  sun. 

The  third  and  much  more  important  case  of  explanation  is 
where  one  law  is  shown  to  be  a  case  of  a  more  general  law. 
As  was  explained  in  Section  I,  we  naturally  discover  the  less 
general  first,  and  gradually  penetrate  to  the  more  simple  but  pro- 
found secrets  of  nature.  It  has  often  been  found  that  scientific 
men  were  in  possession  of  several  well-known  laws  without  peir- 
ceiving  the  bond  which  connected  them  together.  Men,  for 
instance,  had  long  known  that  all  heavy  bodies  tended  to  faU 
towards  the  earth,  and  before  the  time  of  Newton  it  was  known 
to  Hooke,  Huyghens,  and  others,  that  some  force  probably  con- 
nected the  earth  with  the  sun  and  moon.  It  was  Newton, 
however,  who  clearly  brought  these  and  many  other  facts  under 
one  general  law,  so  that  each  fact  or  less  general  law  throws 
light  upon  every  other. 

4.  Pascal  on  Method. 

As  no  treatment  of  the  subject  of  Method  would  be 
complete  without  a  reference  to  Pascal's  rules,  we  here 


268  METHOD. 

add  them  as  prepared  by  him  for  the    Port  Roydi 
Logic: 

1.  To  admit  no  terms  in  the  least  obscure  or  equivo- 
cal without  defining  them. 

2.  To  employ  in  the  definitions  only  terms  perfectly 
known  or  already  explained. 

3.  To  demand  as  axioms  only  truths  perfectly  evi- 
dent 

4.  To  prove  all  propositions  which  are  at  all  obscure, 
by  employing  in  their  proof  only  the  definitions  which 
have  preceded,  or  the  axioms  which  have  been  accorded, 
or  the  propositions  which  have  been  already  demon- 
strated, or  the  construction  of  the  thing  itself  which  is 
in  dispute,  when  there  may  be  any  operation  to  per- 
form. 

5.  Never  to  abuse  the  equivocation  of  terms  by  fail- 
ing to  substitute  for  them,  mentally,  the  definitions 
which  restrict  and  explain  them. 

It  may  be  doubted  whether  any  man  ever  possessed  a  more 
acute  and  perfect  intellect  than  that  of  Blaise  Pascal.  He  was 
bom  in  1633,  at  Clermont  in  Auvergne,  and  from  his  earliest 
years  displayed  signs  of  a  remarkable  character.  His  father 
attempted  at  first  to  prevent  his  studying  geometry,  but  such  was 
Pascal's  genius  and  love  of  this  science,  that,  by  the  age  of 
twelve,  he  had  found  out  many  of  the  propositions  of  Euclid's 
first  book  without  the  aid  of  any  person  or  treatise.  It  is  diflScult 
to  say  whether  he  is  most  to  be  admired  for  his  mathematical 
discoveries,  his  invention  of  the  first  calculating  machine,  his 
wonderful  Provincial  Letters  written  against  the  Jesuits,  or  for 
his  profound  Pensees  or  Thoughts,  a  collection  of  his  retiections 
oo  scientific  and  religious  topics. 

Among  these  Thoughts  is  to  be  found  a  remarkable  fragment 
apon  Logical  method,  the  sabBtaDce  of  which  is  also  given  in  the 


COMPLETE   METHOD.  259 

Port  Royal  Logic.  It  forms  the  second  article  of  the  Pensie* 
and  is  entitled  Reflexions sur  la  Qiometrie en  general.  As  I  knov* 
no  composition  in  which  perfection  of  truth  and  clearness  of  ex 
pression  are  more  nearly  attained,  I  propose  to  give  in  this  Section 
a  free  translation  o*  the  more  important  parts  of  this  fragment, 
appending  to  it  rules  of  method  from  the  Port  Royal  Logic,  and 
from  Descartes'  celebrated  Essay  on  Method.  The  words  of  Pascal 
are  nearly  as  follows : 

"  Tbe  true  method,  which  would  furnish  demonstrations  of  th« 
highest  excellence,  if  it  were  possible  to  employ  the  method 
fully,  consists  in  observing  two  principal,  rules.  The  first  rule  is 
not  to  employ  any  term  of  which  we  have  not  clearly  explained 
the  meaning ;  the  second  rule  is  never  to  put  forward  any  prop- 
osition which  we  cannot  demonstrate  by  truths  already  known  ; 
that  is  to  say,  in  a  word,  to  define  all  the  termn,  and  to  prove  all 
the  propositions.  But,  in  order  that  I  may  observe  the  rules  of 
the  method  which  I  am  explaining,  it  is  necessary  that  I  declare 
what  is  to  be  understood  by  Definition. 

"  We  recognize  in  Geometry  only  those  definitions  which 
logicians  call  Nominal  Definitions,  that  is  to  say,  only  those 
definitions  which  impose  a  name  ujxjn  things  clearly  designated 
in  terms  perfectly  known ;  and  I  speak  only  of  those  definitions." 

Their  value  and  use  is  to  clear  and  abbreviate  discourse  by  ex- 
pressing in  the  single  name  which  we  impose  what  could  not 
be  otherwise  expressed  but  in  several  words :  provided,  neverthe- 
less, that  the  name  imposed  remain  divested  of  any  other  mean 
ing  which  it  might  possess,  so  as  to  bear  that  alone  for  which  we 
intend  it  to  stand. 

"  For  example,  if  we  need  to  distinguish  among  numbers  those 
which  are  divisible  into  two  equal  parts,  from  those  which  are 
not  so  divisible,  in  order  to  avoid  the  frequent  repetition  of  thift 
distinction,  we  give  a  name  to  it  in  this  manner : — we  call  everj 
number  divisible  Into  two  equal  parts  an  Even  Number. 

"  This  is  a  geometrical  definition,  because  after  having  clearlj 
designated  a  thing,  namely  any  number  divisible  into  two  equal 
parts,  we  give  It  a  name  divested  of  every  other  meaning  which 
it  might  have,  in  order  to  bestow  upon  it  the  meaning  de- 
signated. 


260  METHOD. 

"  Hence  it  appears  that  definitions  are  very  free,  and  that  thej> 
can  never  be  subject  to  contradiction,  for  there  is  nothing  more 
allowable,  than  to  give  any  name  we  wish  to  a  thing  which  we 
have  clearly  pointed  out  It  is  only  necessary  to  take  care  ibat 
we  do  not  abuse  this  liberty  of  imposing  names,  by  giving  the 
same  name  to  two  diflFerent  things.  Even  that  would  be  allow- 
able, provided  that  we  did  not  confuse  the  results,  and  extend 
them  from  one  to  the  other.  But  if  we  fall  into  this  vice,  we 
have  a  very  sure  and  infallible  remedy  :  it  is,  to  substitute  men- 
tally the  definition  in  place  of  the  thing  defined,  and  to  hold  the 
definition  always  so  present  in  the  mind,  that  every  time  we 
speak,  for  instance,  of  an  even  number,  we  may  understand  pre- 
cisely that  it  is  a  number  divisible  into  two  equal  parts,  and  so 
that  these  two  things  should  be  so  combined  and  inseparable  in 
thought,  that  as  often  as  one  is  expressed  in  discourse,  the  mind 
may  direct  itself  immediately  to  the  other. 

"  For  geometers  and  all  who  proceed  methodically  only  impose 
names  upon  things  in  order  to  abbreviate  discourse,  and  not  to 
lessen  or  change  the  ideas  of  the  things  concerning  which  they 
discourse.  They  pretend  that  the  mind  always  supplies  the 
entire  definition  of  the  brief  terms  which  they  employ  simply  to 
avoid  the  confusion  produced  by  a  multitude  of  words. 

"  Nothing  prevents  more  promptly  and  effectively  the  insidious 
fallacies  of  the  sophists  than  this  method,  which  we  should  always 
employ,  and  which  ulone  suffices  to  banish  all  sorts  of  difficulties 
and  equivocations. 

"  These  things  being  well  understood,  1  return  to  my  explana- 
tion of  the  true  method,  which  consists,  as  I  said,  in  defining 
everything  and  proving  everything. 

"  Certainly  this  method  would  be  an  excellent  one,  were  it  not 
absolutely  impossible.  It  is  evident  that  the  first  terms  we 
wished  to  define  would  require  previous  terms  to  serve  for  their 
explanation,  and  similarly  the  first  propositions  we  wished  to 
prove,  would  presuppose  other  propositions  preceding  them  in  our 
knowledge ;  and  thus  it  is  clear  that  we  should  never  arrive  at 
the  first  terms  or  first  propositions. 

'Accordingly  in  pushing  our  researchns  further  and  further,  we 
urive  necessarily  at  primitive  words  which   we  cannot  define 


COMPLETE  METHOD.  261 

and  at  principles  so  clear,  that  we  cannot  find  any  principles 
more  clear  to  prove  them  by.  Thus  it  appears  that  men  are 
naturally  and  inevitably  incapable  of  treating  any  science  what- 
ever in  a  perfect  method  ;  but  it  does  not  thence  fellow  that  we 
ought  to  abandon  every  kind  of  method ....  The  most  perfect 
method  available  to  men  consists  not  in  defining  everything  and 
demonstrating  everything,  nor  in  defining  nothing  and  demon- 
etratingr  nothing,  but  in  pursuing  the  middle  course  of  not 
defining  things  which  are  clear  and  understood  by  all  persons, 
but  of  defining  all  others ;  and  of  not  proving  truths  known  to 
all  persons,  but  of  proving  all  others.  From  this  method  they 
equally  err  who  undertake  to  define  and  prove  everything,  and 
they  who  neglect  to  do  it  in  things  which  are  not  self-evident." 

It  is  made  plain  in  this  admirable  passage  that  we  can  never 
by  using  words  avoid  an  ultimate  appeal  to  things,  because  each 
definition  of  a  word  must  require  one  or  more  other  words,  which 
also  will  require  definition,  and  so  on,  ad  infinitum.  Nor  must 
we  ever  return  back  upon  the  words  already  defined  ;  for  if  we 
define  A  by  B,  and  B  by  C,  and  G  by  D,  and  then  2)  by  ^,  we 
commit  what  may  be  called  a  eireulua  in  definiendo;  a  most 
serious  fallacy,  which  might  lead  us  to  suppose  that  we  know 
the  nature  of  A,  B,  0,  and  D,  when  we  really  know  nothing 
about  them. 

5.  Descartes  on  Method. 

We  also  add  here  the  rules  of  the  celebrated  Des- 
cartes for  guiding  the  reason  in  the  attainment  of 
truth.     They  are  as  follows : 

lo  Never  to  accept  anything  as  true,  which  we  do 
not  clearly  know  to  be  so ;  that  is  to  say,  carefully  to 
avoid  haste  or  prejudice,  and  to  comprise  nothing  more 
in  our  judgments  than  what  presents  itself  so  clearly 
and  distinctly  to  the  mind  that  we  cannot  have  any 
room  to  doubt  it. 

2.  To   divide  each   difficulty  we   examine    into  as 


263  HETHOD. 

many  parts  as  possible,  or  as  may  be  required  for  re- 
solving it. 

3.  To  conduct  our  thoughts  in  an  orderly  manner, 
commencing  with  the  most  simple  and  easily  known 
objects,  in  order  to  ascend  by  degrees  to  the  knowledge 
of  the  most  complex. 

4.  To  make  in  every  case  enumerations  so  complete, 
and  reviews  so  wide,  that  we  may  be  sure  of  omitting 
nothing. 

These  rules  were  first  stated  by  Descartes  in  his  admirable 
Discourse  on  Method,  in  which  he  gives  his  reflections  on  the 
right  mode  of  conducting  the  reason,  and  searching  for  truth  in 
any  of  the  sciences.  This  little  treatise  is  easily  to  be  obtained 
in  the  original  French,  and  has  also  been  translated  into  English 
by  Mr.  Veitch.*  Tbe  learner  can  be  strongly  advised  to  study 
it.  Always  to  observe  the  rules  of  Descartes  and  Pascal,  or  to 
know  whether  we  in  every  case  observe  them  properly,  is  im 
possible,  but  it  must  nevertheless  be  valuable  to  know  at  what 
we  ought  to  aim. 

Read  Locke's  brief  Esmy  on  the  Condiict  of  the  Understanding 
which  contains  admirable  remarks  on  the  acquirement  ol 
exact  and  logical  habits  of  thought ;  and  Mr.  Spencer  Baynes' 
Translation  of  the  Port  Royal  Logic,  p.  317  ct  seq. 

In  this  Section,  on  "  Complete  Method,**  we  have 
considered : — 

1.  Empirical  and  Rational  Knowledge. 

2.  The  Elements  of  Complete  Method. 

3.  The  Nature  of  Explanation. 

4.  Pascal  on  Method. 

5.  Descartes  on  Method. 


•  Pnbliflhed  at  Rdinbnigb  in  laSt 


CHAPTEB    ¥1!. 

RECENT    LOGICAL    VIEWS. 

The  principal  part  of  the  preceding  chapters  is  but  a 
restatement  of  what  has  been  taught  as  constituting  the 
science  of  Logic  ever  since  the  days  of  Aristotle.  Some 
additions  have,  indeed,  been  made,  and  they  have  been 
incorporated  with  the  older  doctrines  as  accepted  re- 
sults of  thought  in  this  department  of  knowledge. 
There  are,  however,  certain  other  views  which  have  not 
been  generally  adopted  as  rightly  claiming  a  place  in 
the  science  of  Logic,  but  which,  nevertheless,  are  suffi- 
ciently important  to  deserve  some  attention  from  the 
student  of  this  subject.  These  new  views  may  be  pre- 
sented in  outline  here  in  two  sections :  (1)  The 
Qiiantificafioti  of  the  Predicate;  and  (2) 
Boole's  System  of  Logic. 


SECTION    !♦ 

THE   QUANTIFICATION    OF  THE   PREDICATE. 

1.  Meaning  of  the  Expression. 

To  quantify  the  predicate  is  simply  to  state  whether 
the  whole  or  the  part  only  of  the  predicate  agrees  with 
OP  differs  from  the  subject.     In  this  proposition, 

"All  metals  are  elements," 


264  RECENT   LOGICAL  VIEWS. 

the  subject  is  quantified,  but  the  predicate  is  not;  we 
know  that  all  metals  are  elements,  but  the  proposition 
does  not  distinctly  assert  whether  metals  make  the 
whole  of  the  elements  or  not.  In  the  quantified  propo- 
sition 

**A11  metals  are  some  elements," 

the  little  word  some  expresses  clearly  that  in  reality 
the  metals  form  only  a  part  of  the  elements.  Aristotle 
avoided  the  use  of  any  mark  of  quantity  by  assuming, 
as  we  have  seen,  that  all  affirmative  propositions  have 
a  particulaj  predicate,  like  the  example  just  given  ;  and 
that  only  negative  propositions  have  a  distributed  or 
universal  predicate.  The  fact,  however,  is  that  he  waa 
entirely  in  error,  and  thus  excluded  from  his  system  an 
infinite  number  of  affirmative  propositions  which  are 
universal  in  both  terms.    It  is  true  that — 

"All  equilateral  triangles  are  all  equiangular  triangles," 

but  this  proposition  could  not  have  appeared  in  hie 
system  except  in  the  mutilated  form — 

"All  equilateral  triangles  are  equiangular." 
Such  a  proposition  as 

**  London  is  the  capital  of  England," 
or  **  Iron  is  the  cheapest  metui," 

had  no  proper  place  whatever  in  his  syllogism,  sinct 
both  terms  are  singular  and  identical  with  each  other 
and  both  are  accordingly  universal. 

2.  Conversion  with  a  Quantified  Predicate. 

As  soon  as  we  allow  the  quantity  of  the  predicate  to 
be  stated  the  forms  of  reasoning  become  much  simpli* 


QUANTIFICATION  OP  THE   PBBDICATE.  265 

fied.  We  may  first  consider  the  process  of  conversion. 
In  our  treatment  of  the  subject  it  was  necessary  to 
dirtinguish  between  conversion  by  limitation  and  simple 
conversion.  But  now  one  single  process  of  simple  con- 
veirsion  is  sufficient  for  all  kinds  of  propositions.  Thua 
the  quantified  proposition  of  the  form  A, 

"All  metals  are  some  elements," 
is  simply  converted  into 

' '  Some  elements  are  all  metals. " 
Tho  particular  affirmative  proposition 

"  Some  metals  are  some  brittle  substances  ** 
becomes  by  mere  transposition  of  terms 

"  Some  brittle  substances  are  some  metals." 
The  particular  negative  proposition 

*'  Some  men  are  not  (any)  trustworthy  persons  " 
is  also  converted  into 

"Not  any  trustworthy  persons  are  some  men," 
though  the  result  may  appear  less  satisfactory  in  this 
form  than  in  the  affirmative  form,  as  follows, 

"Some  men  are  some  not-trustworthy  persons," 
converted  simply  into 

"Some  not-trustworthy  persons  are  some  men." 
The  universal  negative   proposition  E  is  converted 
simply  as  before,  and  finally  we  have  a  new  affirmative 
proposition  universal  both   in   subject  and  predicate  ; 
as  in 

"All  equilateral  triangles  are  all  equiangular  triangles," 
which  may  obviously  be  converted  simi)ly  into 
"All  equiangular  triangles  are  all  equilateral  triangles.*' 
18 


266  EEOBITT   LOGICAL   VIEWS. 

This  doubly  universal  affirmative  proposition  is  of 
most  frequent  occurrence ;  as  in  the  case  of  all  defi- 
nitions and  singular  propositions ;  I  may  give  aa  in- 
stances '*  Honesty  is  the  best  policy,"  "  The  greatest 
truths  are  the  simplest  truths,"  "  Virtue  alone  is  hap- 
piness helow,"  "  Self-exaltation  it.  the  fool's  paradise." 

3.  The  Rule  for  Conversion. 

When  affirmative  propositions  are  expressed  in  the 
quantified  form  all  immediate  inferences  can  be  readily 
drawn  from  them  by  this  one  rule,  that  whatever 
we  do  with  one  term  toe  should  do  luith  the  other 
term.  Thus  from  the  doubly  universal  proposition, 
*'  Honesty  is  the  best  policy,"  we  infer  that  "  what  is 
not  the  best  policy  is  not  honesty,"  and  also  "  what  is 
not  honesty  is  not  the  best  policy."  From  this  propo- 
sition in  fact  we  can  draw  two  contrapositives ;  but  the 
learner  will  carefully  remember  that  from  the  ordinary 
unquantified  proposition  A  we  can  only  draw  one  con- 
trapositive  (see  p.  90).  Thus  if  "metals  are  elements" 
we  must  not  say  that  "what  are  not  metals  are  not 
elements."  But  if  we  quantify  the  predicate  thus,  "All 
metals  are  some  elements,"  we  may  infer  that  "  what 
are  not  metals  are  not  some  elements."  Immediate 
inference  by  added  determinant  and  complex  concep- 
tion can  also  be  applied  in  either  direction  to  quanti- 
fied propositions  without  fear  of  the  errors  noticed  in 
pp.  91,  92. 

4.    Number  of  Propositions  with  Quantified 
Predicate. 

It  is  clear  that  in  admitting  the  mark  of  quantity 


QUANTIFICATION  Qf  THE   PREDICATE.  267 

before  the  predicate  we  shall  double  the  number  of 
propositions  which  must  be  admitted  into  the  syllogism, 
because  the  predicate  of  each  of  the  four  propositions 
A,  E,  I,  0  may  be  either  universal  or  particular.  Thus 
we  arrive  at  a  list  of  eight  conceivable  kinds  of  propo- 
sitions, which  are  stated  in  the  following  table : 

U  AllXisalir.  j 

I  Some  X  is  some  Y.  (,     Affirmative 

A  All  X  is  some  Y.  I      propositions. 

Y  Some  X  is  all  F.  ) 

E  NoXis  (any)  Y.  ) 

CO  Some  X  is  not  some  Y.  (      Negative 

ij  No  X  is  some  Y.  C  propositions. 

0  Some  X  is  no  Y.  J 

The  letters  X  and  l^are  used  to  stand  for  any  sub- 
ject and  predicate  respectively,  and  the  learner  by  sub- 
stituting various  terms  can  easily  make  propositions  of 
each  kind.  The  symbolic  letters  on  the  left-hand  side 
were  proposed  by  Arclibishop  Thomson  as  a  convenient 
mode  of  referring  to  each  of  the  eight  propositions, 
and  are  very  suitably  chosen.  The  doubly  universal 
affirmative  proposition  is  called  U  ;  the  simple  con- 
verse of  A  is  called  Y;  the  Greek  letter  rj  (Eta,  e)  is 
applied  to  the  proposition  obtained  by  changing  the 
universal  predicate  of  E  into  a  particular  predicate ;  and 
the  Greek  at  {Omega,  o)  is  applied  to  the  proposition 
similarly  determined  from  O.  All  these  eight  proposi- 
tions are  employed  by  Sir  W.  Hamilton,  but  Archbishop 
Thomson  considers  that  two  of  them,  tj  and  cd,  are 
never  really  used.  It  is  remarkable  that  a  complete 
table  of  the  above  eight  propositions  was  given  by  Mr. 
George  Bentham  in  a  work  called   Outline  of  a  Neit 


368  RECENT  LOGiPAL  VIEWS. 

System  of  Logic,  published  in  1827,  seyeral  years  pre 
vious  to  the  earliest  of  the  logical  publications  of  Sir 
W.  Hamilton.  But  Mr.  Bentham  considered  that  some 
of  the  propositions  are  hardly  to  be  distinguished  from 
others  ;  as  Y  from  A,  of  which  it  is  the  simple  con- 
verse ;  or  Ti  from  0. 

5.  Number  of  Syllogrisnis  with  Quantified 
Predicate. 

The  employment  even  of  the  additional  two  proposi- 
tions (J  and  Y  introduced  by  Thomson  much  extends 
the  list  of  possible  syllogisms,  making  them  altogether 
62  in  number,  without  counting  the  fourth  figure, 
which  is  not  employed  by  Hamilton  and  Thomson. 
When  the  whole  eight  propositions  are  admitted  into 
use  we  are  obliged  to  extend  the  list  of  possible  syllo- 
gisms so  as  to  contain  12  affirmative  and  24  negative 
moods  in  each  of  the  first  three  figures.  The  whole  of 
these  moods  are  conveniently  stated  in  the  table  on 
the  next  page,  given  by  Archbishop  Thomson  at  p.  188 
of  his  Laius  of  Thought. 

6.  Hamilton's  Notation. 

Sir  W.  Hamilton  also  devised  a  curious  system  of 
notation  for  exhibiting  all  the  moods  of  the  syllogism 
in  a  clear  manner.  He  always  employed  the  letter  M 
to  denote  the  middle  term  of  the  syllogism,  and  the 
two  letters  C  and  r  (the  Greek  capital  letter  Gamma) 
for  the  two  terms  appearing  in  the  conclusion. 


QUANTIFICATION  OF  THE   PREDICATE. 


269 


Table  of  Moods  of  the  Syllogism. 


FiBST  FiauBB.       1 

Sicoin) 

PlGITBB. 

Thibd 

F^GUBB. 

Affirm. 

Neg. 

Affirm. 

Neg. 

Affirm. 

Neg. 

1 

UU  U 

EUE 

UEE  I 

uuu 

EUE 

UEE 

UUU 

EU  E 
UEE 

11 

AYI 

)?  Yw 
AOw 

YYI 

OYu 
YOw 

A  AI 

7J  A  u 

A  7?  (J 

m 

AAA 

V  An 

Arm 

YAA 

0  Arj 

Yvv 

AYA 

vYv 
AOti 

Iv 

YYY 

OYO 
YOO 

AYY 

7?Y0 
AOO 

Y  AY 

0  AO 
YEO 

V 

AI  I 

7?  I  W 

A  u  u 

YII 

OIg) 
Y  o  w 

All 

17 1  (•> 
A  u  u 

vi 

lYI 

w  Y  w 
lOw 

lYI 

uYu 
lOu 

I  AI 

u  A  (J 

vii 

UYY 

EYO 
UOO 

UYY 

EYO 
UOO 

U  AY 

E  AO 

viii 

AUA 

v\5v 
AEv 

YUA 

OVv 

YEn 

AUA 

A  E;/ 

ix 

U  AA 

E  AE 

UvJ/ 

i  U  AA 

1 

EAE 

Uvv 

UYA 

EYE 
\J  On 

X 

YUY 

OUO 

YEE 

AUY 

riUO 
A  EE 

YUY 

OUO 
YEE 

xi 

U  II 

EIO 

U  O  6) 

:    UII 

EIO 

U  w  u 

UII 

EIO 

xu 

I  UI 

w  U  u 
IEt; 

lUI 

W  U    (J 

lEri 

lUI 

u  \J  u 

IE7 

The  copula  of  the  proposition  was  indicated  by  a  line  thickened 
towards  the  subject :  thus  (7i^i^""  J/"  meaus  that  "  C  is 

M."  To  indicate  the  quantity  of  the  terms  Hamilton  inserted  a 
colon  {:)  between  the  term  and  the  copula  when  the  quantity  is 
universal,  and  a  comma  (,)  wlien  the  quantity  is  particular.  Thus 
we  readily  express  the  following  affirmative  propositions. 


,M    All  (7 's  are  somen's        (A) 

:  M    All  C's  are  all  if 's  (U) 

,  M    Some  C's  are  some  if's     (I) 


luid  so  on     Any  aflBrmative  proposition  can  be  converted  int* 


270  RECENT  LOGICAL  VIEWS. 

the  corresponding    negative  proposition   by  drawing  a  stiobc 
through  the  line  denoting  the  copula,  as  in  the  following — 

M    No  C  is  any  M  (E) 

M    Some  C  is  not  any  M       (0) 
M    Some  C  is  not  some  M      (w) 

Any  syllogism  can  be  represented  by  placing  M  the  middh 
term  in  the  centre  and  connecting  it  on  each  side  \vith  the  othei 
terms.  The  copula  representing  the  conclusion  can  then  b« 
placed  below ;  Barbara  is  expressed  as  foUows — 

G  ,  M  :  M,  ■■  :  r 


The  negative  mood  Celarent  is  similarly — 

O: 1  I  '.M  , 

J- 


Cesare  in  the  second  figure  is  thus  represented— 

0  :   ■  M  :  I  ■   :  r 

I 

7.  Hamilton's  Canon  of  the  Syllogrlsm. 

Sir  W.  Hamilton  also  proposed  a  new  law  or  supreme 
canon  of  the  syllogism  by  which  the  validity  of  all 
forms  of  the  syllogism  might  be  tested.  This  was 
stated  in  the  following  words  :  "  What  worse  relation 
of  subject  and  predicate  subsists  between  either  of  two 
terms  and  a  common  third  term,  with  which  both  are 
related,  and  one  at  least  positively  so — that  relation 
subsists  between  these  two  terms  themselves." 

By  a  worse  relation,  Sir  William  means  that  a  nejjrative  rela- 
tion is  worse  than  an  affirmative,  and  a  jjnrticular  than  a  universal. 
This  canon  thus  expresses  the  rules  that  if  there  be  a  negative 
premise  the  conclusion  must  be  negative,  and  if  there  be  a  par 


QUANTIFICATION  OF  THE   PREDICATE.  271 

tieolar  premise  the  conclusion  must  be  particular.  Special  canons 
were  also  developed  for  each  of  the  three  figures,  but  in  thus 
rendering  the  system  complex  the  advantages  of  the  quantified 
form  of  proposition  seem  to  be  lost. 

Prof.  De  Morgan  also  discovered  the  advantages  of  the  quanti 
fied  predicate,  and  invented  a  system  diflfering  greatly  from  that 
of  Sir  W.  Hamilton.  It  is  fully  explained  in  his  Formal  Logic, 
The  SyUabus  of  a  new  System  of  Logic,  and  various  important 
memoirs  on  the  Syllogism  in  the  Transactions  of  the  Cambridge 
Philosophical  Society.  In  these  works  is  also  given  a  complete 
explanation  of  the  "Numerically  Definite  Syllogism."  Mr.  De 
Morgan  pointed  out  that  two  particular  premises  may  often  give 
a  valid  conclusion  provided  that  the  actual  quantities  of  the  two 
terms  are  stated,  and  when  added  together  exceed  the  quantity  of 
the  middle  term.  Thus  if  the  majority  of  a  public  meeting  vote 
for  the  first  resolution,  and  a  majority  also  vote  for  the  second, 
it  follows  necessarily  that  some  who  voted  for  the  first  voted  also 
for  the  second.  The  two  majorities  added  together  exceed  the 
whole  number  of  the  meeting,  so  that  they  could  not  consist  of 
entirely  different  people  They  may  indeed  consist  of  exactly 
the  same  people  ;  but  all  that  we  can  deduce  from  the  premises 
is  that  the  excess  of  the  two  majorities  added  together  over  the 
number  of  the  meeting  must  have  voted  in  favor  of  each  resolu- 
tion. This  kind  of  inference  has  by  Sir  VV.  Hamilton  been  said 
to  depend  on  ultra-total  distribution  ;  and  the  name  of  Plurative 
Propositions  has  been  proposed  for  all  those  which  give  a  dis- 
tinct idea  of  the  fraction  or  number  of  the  subject  involved  in  the 
assertion. 

T.  Spencer  Baynes,  Essay  on  the  new  Analytic  of  Logical 

Forms  ;  Edinburgh,  1850. 
Prof.  Bowen's  Treatise  on  Logic  or  t?ie  Laics  of  Pure  ThougJit, 

Cambridge,  Mass.,  1866,  gives  a  full  and  excellent  account  cf 

Hamilton's  Logic. 
Bee  also  Hamilton's  Lectures  on  Logic,  New  York,  185& 


272  RECENT  LOGICAL  VIEWS. 

In  this  Section^  on  '*Tlic  Quantification  of  the 
Predicate,"  we  liave  considered : 

1.  Meaning  of  the  Expression. 

2.  Conversion  with  ii  Quantified  Predicate, 

3.  Tlie  Rale  for  Conversion. 

4.  Number  of  Propositions  with  Quantified  Pred- 

icate. 

5.  Number  of  Syllogisms  with  Quantified  Pred^ 

icate. 

6.  Hatnilton's  Notation. 

7.  Hatnilton's  Cation  of  the  Syllogism, 


SECTION    IL 
BOOLE'S   SYSTEM    OF   LOGIC. 

1.  The  Difficulty  of  Dr.  Boole's  Statement. 

It  would  not  be  possible  to  give  in  an  elementary  work 
a  notion  of  the  system  of  indirect  inference  first  dis- 
covered by  the  late  Dr.  Boole,  the  Professor  of  Mathe- 
matics at  the  Queen's  College,  Cork.  This  system  was 
founded  upon  the  Quantification  of  the  Predicate,  but 
Dr.  Boole  regarded  Logic  as  a  branch  of  Mathematics, 
and  believed  that  he  could  arrive  at  every  possible 
inference  by  the  principles  of  algebra.  The  proc  ss  as 
actually  employed  by  him  i^  very  obscure  and  difficult; 
and  hardly  any  attempt  to  introduce  it  into  elementary 
text-books  of  Logic  has  yet  been  made. 

I  have  been  able  to  arrive  at  exactly  the  same  results 
as  Dr.  Boole  without  the  use  of  any  mathematics;  and 
though  the  very  simple  process  which  I  am  going  to 
describe  can  hardly  be  said  to  be  strictly  Dr.  Boole's 


BOOLE'S  SYSTEM   OF  LOGIC.  27'a 

logic,  it  is  yet  very  similar  to  it  and  can  prove  every- 
thing that  Dr.  Boole  proved.  This  Method  of  Indirect 
Inference  is  founded  upon  the  three  primary  Laws  of 
Thought,  and  the  learner  who  may  have  thought  them 
mere  useless  truisms  will  perhaps  be  surprised  to  find 
how  extensive  and  elegant  a  system  of  deduction  may 
be  derived  from  them, 

2.  Application  of  the  Law  of  Excluded  Middle. 

The  Law  of  Excluded  Middle  enables  us  to  assert 
that  anything  must  either  have  a  given  quality  or  must 
have  it  not.  Thus  if  iron  be  the  thing,  and  co^nbusii- 
bility  the  quality,  any  one  must  see  that 

"Iron  is  either  combustible  or  incombustible." 

This  division  of  alternatives  may  be  repeated  as  often 
as  we  like.  Thus  let  book  be  the  class  of  things  to  be 
divided,  and  English  and  Scientific  two  (jualities.  Then 
any  book  must  be  either  English  or  not  English ;  again 
an  English  book  must  be  either  Scientific  or  not  Scien- 
tific, and  the  same  may  be  said  of  books  which  arc  not 
English.  Thus  we  can  at  once  divide  books  into  four 
classes — 

Books,  English  and  Scientific. 
Books,  English  and  not-Scientific. 
Books,  not-English  and  Scientific. 
Books,  not-English  and  not-Scientific. 

This  is  what  we  may  call  an  exhaustive  division  of 
<.he  class  books;  for  there  is  no  possible  book  which 
iocs  not  fall  into  one  division  or  other  of  these  four, 
for  the  simple  reason,  that  if  it  does  not  fall  into  any  oi 
uhe  first  three  it  must  fall  into  the  last.     The  process 


274  EECElfT  LOGICAL   VIEWS. 

can  be  repeated  without  end,  as  long  as  any  new  ci^ 
cumstance  can  be  suggested  as  the  ground  of  division. 
Thus  we  might  divide  each  class  again  according  as  the 
books  are  octavo  or  not  octavo,  bound  or  unbound, 
published  in  London  or  elsewhere,  and  so  on.  We 
shall  call  this  process  of  twofold  division,  which  is 
really  the  process  of  Dichotomy,  the  development  of  a 
term,  because  it  enables  us  always  to  develop  the  utmost 
number  of  alternatives  whicli  need  be  considered. 

3.  Application  of  the  Law  of  Coutradiction. 

As  a  general  rule  it  is  not  likely  that  all  the  alterna- 
tives thus  unfolded  or  developed  can  exist,  and  the  next 
point  is  to  ascertain  how  many  do  or  may  exist.  The 
Law  of  Contradiction  asserts  that  nothing  can  combine 
contradictory  attributes  or  qualities,  and  if  we  meet 
with  any  term  which  is  thus  self-contradictory  we  are 
authorized  at  once  to  strike  it  out  of  the  list.  Now 
consider  our  old  example  of  a  syllogism  : 

Iron  is  a  metal ; 

All  metals  are  elements  ; 

Therefore  iron  is  an  element. 

We  can  readily  prove  this  conclusion  by  the  indirect 
method.  For  if  we  develop  the  term  iron,  we  have  foul 
alternatives;  thus — 

Iron,  metal,  element. 

Iron,  metal,  not-element. 

Iron,  not-metal,  element 

Iron,  not-metal,  not-element. 

But  if  we  compare  each  of  these  alternatives  with  the 
premises  of  the  syllogism,  it  will  be  apparent  that 


BOOLES'  SYSTEM  OF  LOQIO.         276 

several  of  them  are  incapable  of  existing.  Iron,  we  are 
informed,  is  a  metal.  Hence  no  class  of  things  **  iron, 
not-metal "  can  exist.  Thus  we  are  enabled  by  the  first 
premise  to  strike  out  both  of  the  last  two  alternatives 
which  combine  iron  and  not-metal.  The  second  alter- 
native, again,  combines  metal  and  not-eleraent;  but  as 
the  second  premise  informs  us  that  "all  metals  are 
elements,"  it  must  be  struck  out.  There  remains,  then, 
only  one  alternative  which  is  capable  of  existing  if  the 
premises  be  true,  and  as  there  cannot  conceivably  be 
more  alternatives  than  those  considered,  it  follows  dem- 
onstratively that  iron  occurs  only  in  combination  with 
the  qualities  of  metal  and  element,  or,  in  brief,  that  it 
is  an  element. 

4.  Universality  of  the  Method. 

We  can,  however,  prove  not  only  the  ordinary  syllo- 
gistic conclusion,  but  any  other  conclusion  which  can 
be  drawn  from  the  same  premises  ;  the  syllogistic  con- 
clusion is  in  fact  only  one  out  of  many  which  can 
usually  be  obtained  from  given  premises.  Suppose,  for 
instance,  that  we  wish  to  know  what  is  the  nature  of 
the  term  or  class  not-element,  so  far  as  we  can  learn 
it  from  the  premises  just  considered.  We  can  develop 
the  alternatives  of  this  term,  just  as  we  did  those  of 
iron,  and  get  the  following — 

Not-element,  iron,  metal. 
Not-element,  iron,  not-metal. 
Not-element,  not-iron,  metal. 
Not-element,  not-iron,  not-metah 

Compare  these  combinations  as  before  with  the  prera- 


276  EECEirr  logical  views. 

ises.  The  drst  it  is  easily  seen  cannot  exist,  because 
all  metals  are  elements  ;  for  the  same  reason  the  third 
cannot  exist ;  the  second  is  likewise  excluded,  because 
iron  is  a  metal  and  cannot  exist  in  combination  with 
the  qualities  of  not-metal.  Hence  there  remains  onlj 
one  combination  to  represent  the  class  desired — namely, 
Not-elemeut,  not-iron,  not-metal. 
Thus  we  learn  from  the  premises  that  every  not- 
element  is  not  a  metal  and  is  not  iron. 

As  another  example  of  this  kind  of  deductive  process 
I  will  take  a  case  of  the  Disjunctive  Syllogism,  in  the 
negative  mood,  as  follows: 

A  fungus  is  either  plant  or  animal, 
A  fungus  is  not  an  animal ; 
Therefore  it  is  a  plant. 

Now  if  we  develop  all  the  possible  ways  in  which 
fungus,  plant  and  animal  can  be  combined  together, 
we  obtain  for  the  term  fungus — 

(1)  Fangus,  plant,  animal. 

(2)  Fungus,  plant,  not-animal. 

(3)  Fungus,  not^i)lant,  animal. 

(4)  Fungus,  not-plant,  not-animal. 

Of  these,  however,  the  4th  cannot  exist  because  by 
the  premise  a  fungus  must  be  a  plant,  or  if  not  a  plant 
an  animal.  The  first  and  3d  again  cannot  exist  because 
the  minor  premise  informs  us  that  a  fungus  is  not  an 
animal.  There  remains  then  only  the  second  combi- 
nation, 

Fungus,  plant,  not^animal, 
from  which  we  learn  the  syllogistic  conclusion  that  "a 
fungus  is  a  plant" 


BOOLE'S  SYSTEM  OF  LOGIC.  277 

5.  Comparative  Excellence  of  the  System. 

The  chief  excellence  of  this  mode  of  deduction  con- 
gists  in  the  fact  that  it  is  not  restricted  to  any  definite 
series  of  forms  like  the  syllogism,  but  is  applicable, 
without  any  additional  rules,  to  all  kinds  of  proposi- 
tions or  problems  which  can  be  conceived  and  stated, 
There  may  be  any  number  of  premises,  and  they 
may  contain  any  number  of  terms  ;  all  we  have  to  do 
to  obtain  any  possible  inference  is  to  develop  the  term 
required  into  all  its  alternatives,  and  then  to  examine 
how  many  of  these  agree  with  the  premises.  What 
remain  after  this  examination  necessarily  form  the 
description  of  the  term.  The  only  inconvenience  of 
the  method  is  that,  as  the  number  of  terms  increases, 
the  number  of  alternatives  to  be  examined  increases 
very  rapidly,  and  it  soon  becomes  tedious  to  write  them 
all  out.  This  work  may  be  abbreviated  if  we  substitute 
single  letters  to  stand  for  the  terms,  somewhat  as  in 
algebra;  thus  we  may  take  A,  B,  C,  D,  etc.,  to  stand 
for  the  aflBrmative  terms,  and  a,  h,  c,  d,  etc.,  for  the 
corresponding  negative  ones. 

Let  us  take  as  a  first  example  the  premises — 
Organic  substance  is  either  vegetable  or  animal. 
Vegetable  substance  consists  mainly  of  carbon,  hydrogen,  and 

nitrogen. 
Animal  substance  consists   mainly  of   carbon,   hydrogen,   and 
nitrogen. 

It  would  take  a  long  time  to  write  out  all  the  combinations  of 
ihe  four  terms  occurring  in  the  above  ;  but  if  we  substitute  letters- 
r&  follows — 

A  =  organic  substance, 
B  =  vegetable  substance, 
0  =  animal  substance, 
D  =  consisting  mainly  of  carbon,  hydrogen,  and  nitrogen. 


278  BEOENT  LOGICAL  VIEWS. 

we  can  readily  represent  all  the  combinations  which  can  belonf 
to  the  term  A. 


(1) 
(3) 
(8) 

(4) 

ABCD 
ABCd 
ABcD 
ABcd 

AbCD 
AbCd 
AbcD 
Abed 

(6) 

(6) 

(7) 
(8) 

Now  the 

premises  amount  to  the  statementc 

i,  that 

A  must  be  either  B  or  0, 
B  must  be  D, 
C  must  be  D. 

The  combinations  (7)  and  (8)  are  Inconsistent  with  the  firs* 
premise ;  the  combinations  (2)  and  (4)  with  the  second  premise; 
and  (6)  is  inconsistent  with  the  third  premise.  There  remain 
jnly, 

ABCD 
ABcD 
AbCD. 

Whence  we  learn  at  once  that  "  organic  substance  (A)  always 
consists  mainly  of  carbon,  hydrogen  and  nitrogen,"  because  it 
always  occurs  in  connection  with  D.  The  reader  may  perhaps 
notice  that  the'  term  ABCD  implies  that  organic  substance  may 
be  both  vegetable  (B)  and  animal  (C).  If  the  first  premise  be 
interpreted  as  meaning  that  this  is  not  possible,  of  course  this 
combination  should  also  he  struck  out.  It  is  an  unsettled  pomt 
whether  the  alternatives  of  a  disjunctive  proposition  can  coexist 
or  not  (see  p.  157),  but  1  much  prefer  the  opinion  that  they  can  ; 
and  as  a  matter  of  fact  it  is  quite  likely  that  there  exist  very 
simple  kinds  of  living  beings,  which  cannot  be  distinctly  asserted 
to  be  vegetable  only  or  animal  only,  but  partake  of  the  nature  of 
each. 

As  a  more  oomplicated  problem  to  show  the  powerE  of  this 
system,  let  us  consider  the  premises  which  were  treated  by  Dr. 
Boole  in  his  Laws  of  Thought,  p.  125,  as  follows : 

"Similar  figures  consist  of  all  whose  corresponding  anfjles  are 
equal,  and  whose  corresponding  sides  are  proportional. 

Triangles  whose  corresponding  angles  are  equal  bftTW  *helb 
corresponding  sido*  proportional ;  and  vies  veraH. 


BOOLE'S  SYSTEM   OF   LOGIC.  279 

Triangles  whose  corresponding  sides  are  proportional   havif 
their  corresponding  angles  equal." 
Now  if  we  take  our  symbol  letters  as  follows : 
A  =  similar  figure, 
B  =  triangle, 

C=  having  corresponding  angles  equal, 
D=  having  corresponding  sides  proportional, 

the  premises  will  be  seen  to  amount  to  the  statements  that 

A  is  identical  with  CD, 
and  that 

BO  ia  identical  with  BD; 

in  other  words,  all  ^'s  ought  to  be  CD'b,  0D'»  ought  to  be  A\ 
all  BG'a  ought  to  be  Blfa  and  all  BD's  ought  to  be  BG's. 

The  possible  combinations  in  which  the  letters  may  be  united 
are  16  in  number  and  are  shown  in  the  following  table: 


ABOD 

aBGD 

ABGd 

aBOd 

ABcD 

aBcD 

ABcd 

aAcD 

AbOD 

abGB 

AhGd 

ahGd 

AbeD 

abcD 

Abed 

abed 

Comparing  each  of  these  combinations  with  the  "premise,  we  see 
that  ABGd,  ABcD,  ABcd,  and  others,  are  to  be  struck  out  be- 
cause every  A  is  also  to  be  GD.  The  combinations  cBGD  and 
obGD  are  struck  out  because  every  GD  should  also  be  A.  Again, 
aBGd  is  inconsistent  with  the  condition  that  every  BG  is  also  to 
be  BD  ;  and  if  the  learner  carefully  follows  out  the  same  process 
of  examination,  there  will  remain  only  six  combinations,  whicL 
agree  with  all  the  premises,  thus — 

ABGD  aBed 

AbOD  abOd 

abeD 
abed 

From  these  combinations  we  can  draw  any  description  we  like  of 


280  EECENT  LOGICAL   VIEWS. 

the  classes  of  things  agreeing  with  the  premises.  The  class  A  oi 
similar  figures  is  represented  by  only  two  combinations  or  alter- 
natives ;  the  negative  class  a  or  dissimilar  figures,  by  four  com- 
binations, whence  we  may  draw  the  following  conclusion:  "  Dis- 
similar figures  consist  of  all  triangles  which  have  not  their 
corresponding  angles  equal,  and  sides  proportional  (aBcd),  and  of 
all  figures,  not  being  triangles,  which  have  either  their  angles 
equal  and  sides  not  proportional  {ctbCd),  or  their  corresponding 
sides  proportional  and  angles  not  equal  (abcD),  or  neither  their 
corresponding  angles  equal  nor  corresponding  sides  proportional 
(abed)." 

6.  The  Liog^ical  Abacus  and  the  Logrical  Machine. 

In  performing  this  method  of  inference  it  is  soon 
seen  to  proceed  in  a  very  simple  mechanical  manner, 
and  the  only  inconvenience  is  the  large  number  of 
alternatives  or  combinations  to  be  examined.  I  have, 
therefore,  devised  several  modes  by  which  the  labor  can 
be  decreased ;  the  simplest  of  these  consists  in  engrav- 
ing the  series  of  16  combinations  on  the  opposite  page, 
which  occur  over  and  over  again  in  problems,  with 
larger  and  smaller  sets,  upon  a  common  writing  slate, 
so  that  the  excluded  ones  may  be  readily  struck  out 
with  a  common  slate  pencil,  and  yet  the  series  may  be 
employed  again  for  any  future  logical  question.  A 
second  device,  which  I  have  called  the  "  Logical  aba- 
cus," is  constructed  by  printing  the  letters  upon  slips 
of  wood  furnished  with  pins,  contrived  so  that  any  part 
or  class  of  the  combinations  can  be  picked  out  mechani- 
cally with  very  little  trouble  ;  and  a  logical  problem  is 
thus  solved  by  the  hand,  rather  than  by  the  head. 
More  recently,  however,  I  have  reduced  the  system  to 
a  completely  mechanical  form,  and  have  thus  embodied 
the  whole  of  the  indirect  process  of  inference  in  what 


BOOLE'S  SYSTEM   OF   LOGIC.  2BI 

may  be  called  a  Logical  Machine.  In  the  front  of  the 
machine  are  seen  certuin  movable  wooden  rods  carry- 
ing the  set  of  16  corabiniitions  of  letters  which  are 
seen  on  page  279.  At  the  foot  are  21  keys  like 
those  of  a  piano;  eight  keys  towards  the  left  hand 
are  marked  with  the  letters  A,  a,  B,  b,  0,  c,  D,  d,  and 
are  intended  to  represent  these  terms  when  occurring 
in  the  subject  of  a  proposition.  Eight  other  keys 
towards  the  right  hand  represent  the  same  letters  or 
terms  when  occurring  in  the  predicate.  The  copula  of 
a  proposition  is  represented  by  a  key  in  the  middle  of 
the  series ;  the  full  stop  by  one  to  the  extreme  right, 
while  there  are  two  other  keys  which  serve  for  the  dis- 
junctive conjunction  or,  according  as  it  occurs  in  sub- 
ject or  predicate.  Now  if  the  letters  be  taken  to  stand 
for  the  terms  of  a  syllogism  or  any  other  logical  argu- 
ment, and  the  keys  of  the  instrument  be  pressed 
exactly  in  the  order  corresponding  to  the  words  of  the 
premises,  the  16  combinations  will  be  so  selected  and 
arranged  thereby  that  at  the  end  only  the  possible  com- 
binations will  remain  in  view.  Any  question  can  then 
be  asked  of  the  machine,  and  an  infallible  answer  will 
be  obtained  from  the  combinations  remaining.  The 
internal  construction  of  the  machine  is  such,  therefore, 
as  actually  to  perform  the  work  of  inference  whicli,  in 
Dr.  Boole's  system,  was  performed  by  a  very  compli- 
cated mathematical  calculation.  It  should  be  added, 
that  there  is  one  remaining  key  to  the  extreme  left 
which  has  the  effect  of  obliterating  all  previous  opera- 
tions and  restoring  all  the  combinations  to  their  original 
place,  so  that  the  machine  -is  then  ready  for  the  per- 
formance of  any  new  problem. 


282  RECENT  LOGICAL  VIEWS. 

An  account  of  this  logical  machine  may  be  foand  in  the  Pro- 
ceedings  of  the  Royal  Society  for  Jan.  20th,  1870,  the  machine 
having  on  that  day  been  exhibited  in  action  to  the  Fellows  of  the 
Society.  The  principles  of  the  method  of  inference  here  described 
are  more  completely  stated  in  The  Siibstitntion  of  Similars*  and 
the  Pure  Logic,\  which  I  published  in  the  years  1869  and  1864. 
I  may  add,  that  the  first-named  of  these  works  contains  certain 
views  as  to  the  real  nature  of  the  process  of  inference  which  I  do 
not  think  it  desirable  to  introduce  into  an  elementary  work  like 
the  present,  on  account  of  their  speculative  character.  The  pro- 
cess of  inference,  on  the  other  hand,  which  I  have  derived  from 
Boole's  system,  is  ol  so  self-evident  a  character,  and  is  so  clearly 
proved  to  be  true  by  its  reduction  to  a  mechanical  form,  that  I  do 
not  hesitate  to  bring  it  to  the  learner's  notice. 

George  Boole,  Mathematical  Analysis  of  Logic,  1847. 
An  Investigation  of  the  Laws  of  Thought.    Londor,  Walton  & 
Maberly,  1854. 

In  this  section,  on  "Boole's  System  of  Logic,'* 
we  have  considered  :— 

1.  T?ie  Difficulty  of  Dr.  Boole* 8  Statetneiit. 

2.  Application  of  the  Law  of  Excluded  Middle, 

3.  Application  of  the  Law  of  Coufradictiou. 

4.  Universality  of  the  Method 

5.  Comparative  Excellence  of  the  System. 

O.  The  Lof/ical  Abacus  and  the  Logical  Machine, 


*  The  SubgtUutUm  of  SlmUar$  the  true  Principle  qf  Reasoning,  derived  from 
a  modificatUmof  ArititotWs  Dictum.    Macmillao  &  Co.,  1869. 

t  Pure  Logic,  or  the  Logic  qf  Quality  apart  from  (Quantity,  etc.  Edwut 
Btanford,  Charing  Croea. 


Sfes^isft, 


AHQ  ouESTmns. 


INTRODUCTION. 

1.  What  is  the  definition  of  Logic  ? 

2.  What  are  the  meanings  of  a  Law  of  Nature,  and  a  Law  ol 

Thought? 
8.  Explain  the  distinction  Ijetween  the  Form  of  Thought,  a.'^d 
the  Matter  of  Thought. 

4.  In  what  sense  may  Logic  be  called  the  Science  of  Sciences? 

5.  How  does  a  Science  differ  from  an  Art,  and  why  is  Logic  more 

in  the  form  of  a  Science  than  an  Art  ? 

6.  Can  we  say  that  Logic  is  a  necessary  aid  in  correct  reasoning, 

when  persons  who  have  never  studied  logic  reason  cor- 
rectly ? 

7.  Name  the  parts  of  which  a  syllogism  is  composed. 

8.  How  far  is  it  correct   to  say  that   Logic   is   concerned  with 

language  ? 

9.  What  are  the  three  acts  of  mind  considered  in  Logic?  Which 

of  them  is  more  especially  the  subject  of  the  Science? 

10.  Can  you  state  exactly  what  is  meant  by  a  general  notion, 
idea,  or  conception  ? 

'1.  How  do  the  Nominalists,  Realists,  and  Conceptualists  diflfei 
in  their  opinions  as  to  the  nature  of  a  general  notion  ? 


1284  tSXEUCliSES  AND   QUESTIONS. 

CHAPTER  X. 

TERMS. 


SECTION    1. 

THE  VARIOUS  KINDS  OF  TERMS 

1.  Define  a  name  or  term. 

2.  What  is  a  categoroniatic  term  ? 

8.  Explain  the  diatinciion  between  a  collective    jtiid  a  general 

term. 
4.  Distinguish  the  collective  and  distributive  use  of  the  word  aH 

in  the  following  : — 

(1)  Non  omnia  moriar  (t.  e.  I  shall  not  all  die). 

(2)  "All  men  find  their  own  in  all  men's  good. 

And  all  men  join  in  noble  brotherhood." 

Tennpson. 

(8)  Non  onmia  possumus  omnes  (/.  e.  we  cannot  all  do  all 

things). 

6.  Which  of  the  following  are  alwtract  terms? 

Act,  ingratitude,  home,  houriv,  homeliness,  introduction, 
individuality,  truth,  true,  trueness,  yellow,  yellowness, 
childho<jd,  book,  blue,  intention,  reason,  rationality,  reason- 
ableness. 

6.  Define  a  negative  term,  and  mention  the  mark  by  which  you 

may  recognize  it. 

7.  Distinguish  a  privative  from  a  negative  term,  and  find  some 

instances  of  privative  terms. 

8.  Describe  tlie  logical  characters  of  the  following  terms,  with 

the  precautions  given  at  p.  28  : 


TERMS. 


285 


Metropolis 

Consciousness 

Sect 

Book 

Lord  Ciiancellor 

Nation 

Library 

Vegetable  Kingdom 

Institution 

Qreat  Britain 

Brilliance 

Light 

Ceesar 

Weight 

Observation 

Void 

Sensation 

Tongue 

Gold 

Ceesar 

Air 

Prime  Minister 

Csesarism 

Mentor 

Indigeslibility 

Application 

Anarchy 

Mancliester 

Individual 

Retribution 

Recollection 

Volume 

Solemnity 

Insignificant 

Language 

Understanding 

Brilliant 

Adornment 

Geology 

Independencfi 

Agreement 

Demeanor 

Heaviness 

Obliquity 

Resemblance 

Illustration 

Motionless 

Departure 

Section 

Henry  VIII. 

Nestor 

Whiteuesa 

Formal  Logic 

Alexander 

SECTION    II, 


THE    AMBIGUITY    OF    TERMS 


1.  Define  univocal  terms,  and  suggest  some  terms  which  are  per 

fectly  univocal. 

2.  What  are  the  other  names  by  which  equivocal  terms  are  often 

called  ? 

3.  Distinguish   the  three  kinds  of  ambiguous  terms,  and  find 

instances  of  each. 

4.  Distinguish  the  three  causes  by  which  the  third  and  most  im 

portant  class  of  ambiguous  terms  have  been  produced. 

5.  Explain  the  ambiguity  of  any  of  the  following  terms,  referring 

each  to  its  proper  cause,  and  tracing  out  as  far  as  possible 
the  derivation  of  each  separate  meaning  from  the  original 
meaning. 


286 


EXERCISES   AND   QUESTIONS. 


BUI 

Minister 

Subject 

Letter 

Table 

Qerk 

Object 

Star 

Term 

Order 

Earth 

Pole 

School 

Wood 

Law 

Reason 

Air 

BoU 

Sensatiou 

Bed 

Glass 

Volume 

Art 

Bowl 

Peer 

Scale 

Interest 

End 

Sense 

Feeling 

Paper 

Division 

Ball 

Kind 

Bolt 

Class 

SECTION     III, 


EXTENSION    AND    INTENSION. 


1.  Distinguish  very  carefully  the  meanings  in  extension  and  in 

tension  of  the  terms — 
Quadruped,  railway,  human  being,  engine,  mountain,  Mem- 
ber of  Parliament. 

2.  Elnumerate  tbe  synonyms  or  other  names  used  instead  of  ex- 

tension  and  intension. 
8.  According  to  wliat  law  is  the  quantity  of  extension  connected 
with  the  quantity  of  intension  1    Show  that  the  law  holds 
true  of  the  following  series  of  terms — 

(1)  Iron,  metal,  element,  matter,  substance. 

(2)  Matter,  organized  matter,  animal,  man. 

(8)  Ship,  steamship,   screw  steamship,   iron   screw-steamship, 

British  iron  screw-steamship. 
(4)  Book,  printed  book,  dictionary,  Latin  dictionary, 
4.  Distinguish  between  the  connotation  and  denotation  of  a  term. 
6.  Select   from   the  list  of  terms  under   Section  I.,  Question  8 
(p.  285),  such  terms  a.s  are  non-con notative  according  to  Mr. 
Mill's  views. 
•    Arrange  the  following  terms  in  series  as  in  Question  8,  placing 
each  term  of  greater  extension  before  a  term  of  less  exten- 
sion.    Point  out  which  are  the  terms  of  greatest  and  least 
intension  in  each  series. 


TEBMS. 


287 


Emperor 

Teacher 

Baptist 

Timber 

Person 

Horse 

Heavenly  bodj 

Christian 


Animal 

Dissenter 

Individual 

Jupiter 

Ruler 

Organized  substance 

Lawyer 

Alexander 


Planet 

Mammalian 

Matter 

Solicitor 

Quadruped 

Being 

Napoleon  III. 

Episcopalian 


SECTION    IV. 

THE    GROWTH    OF    LANGUAGE. 

1.  Trace  out  the  generalization  or  specialization  which  has  taken 
place  in  any  of  the  following  words : 
Kind,  genus,  class,  species,  order,  rank,  Augustus,  president, 
speaker,  Utopia,  rock,  Commons,  doctor. 
8.  Point  out  metaphors  derived  from   the  notions  of  weight, 

straightness,  rock,  wind. 
8.  Distinguish  as  accurately  as  possible  the  meanings  of  the  fol- 
lowing synonyms : — 
Sickness,     malady;     mud,    mire;      confutation,    refutation; 
boundary,    imit ;    mind,    intellect ;   recollection,  reminis- 
cence;   procrastination,    dilatoriness;    converse,    reverse, 
obverse,  inverse. 
4.  Form  lists  of  all  the  words  derived  from  any  of  the  following 
roots: — 

(1)  Tendere,  to  stretch,  as  in  intention,  attention. 

(2)  Poiiere,  to  place,  as  in  position,  supposition. 

(3)  Genus,  tribe  or  kind,  as  in  genus,  generation. 

(4)  Munus,  gift,  as  in   remuneration,   common    (Latin,    Oom 

munis). 

(5)  Modus,  shape  or  fashion,  as  in  mood,  moderate. 

(6)  Scribere,  to  write,  as  in  scribe,  inscription,  describe, 

(7)  Capere  to  take,  as  in  deception,  incipient. 


888  EXERCISES   AND   QUESTIONS. 


SECTION    V, 

THE    PERFECT   AND   THE    IMPERFECT    KNOWLEDGE    OF 
TERMS. 

1.  What  are  the  characters  of  perfect  knowledge  ? 
&  Describe  the  character  of  the  knowledge  which  we  have  of  the 
following  notions  or  objects : — 

A  syllogism. 

Electricity. 

Motion. 

A  triangle. 

Eternity. 

The  weight  of  the  e,arth  (5852  trillions  of  tons). 

The  color  of  the  sKy. 
8.  EiXplain  exactly  what  you  mean  by  intuitive  knowiadga 


CHAPTER    II. 
PROPOSITIONS. 


SECTION    I. 

THE   KINDS   OF    PROPOSITIONS. 

1.  Define  a  proposition,  and  name  the  parts  of  which  ^t  is  com- 
posed. 

3.  How  are  propositions  classified  ? 

8.  Name  the  four  kinds  of  categorical   propositions,  and  theii 
symbols. 

4.  Under  which  classes  arc  singular  and  indefinite  propositiont 

placed? 
i.  Enumerate  the  most  usual  signs  of  the  quantity  of  a  i  roDosi 
tkm. 


PROPOSITIONS.  289 

8.  What  are  modal  propositions  according  to  early  logicians,  and 

according;  to  Thomson  ? 
7.  How  far  do  logicians  consider  propositions  witli  regard  to  their 

truth  or  falsity? 


SECTION    II. 

OPPOSITION     OF     PROPOSITIONS. 

1.  State  ,he  quantity  of  the  subject  and  predicate  in  each  of  th« 

propositions  A,  E,  I,  0. 

2.  Select  out  of  the  following  propositions,  pairs  of  contrary, 

contradictory,  subaltern,  and  subcoutrary  propositions  • — 

(1)  Some  elements  are  known. 

(2)  No  elements  are  known. 

(3)  All  elements  are  known. 

(4)  Not  all  elements  are  known. 

(5)  Some  elements  are  not  known 

(6)  All  elements  are  not  known. 

&  What  propositions  are  true,  false,  or  doubtful, 

(1)  when  A  is  false,  (3)  when  I  is  false, 

(2)  when  E  is  false,  (4)  when  0  is  false  ? 

4.  Prove  by  means  of  the  contradictory  propositions  that  subcon- 

trary  propositions  cannot  both  be  false. 

5.  Show  by  means  of  the  subcontrary  projxjsitions  that  contrary 

propositions  may  both  be  false. 
9.  What  quantity  would  you  assign  to  each  of  the  following 
propositions  ? 

(1)  Knowledge  is  power. 

(2)  Nebulae  are  material  bodies. 

(3)  Light  is  the  vibration  of  an  ether. 

(4)  Men  are  more  to  be  trusted  than  we  think. 

(5)  The  Chinese  are  industrious 

*.  Why  is  it  desirable  in  controversy  to  refute  a  statement  by  its 
contradictory  and  not  by  its  contrary? 


8W  EXEBCISBS  AND  QUESTIONS. 

SECTION    III. 

CONVERSION    AND    IMMEDIATE    INFERENCE. 

1.  Define  inference  and  conversion. 

2.  What  are  converse  and  convertend  propositions? 
8.  State  the  ruk-a  of  valid  conversion. 

4-  Name  all  the  kinds  of  conversion. 

6.  By  what  process  do  we  pass  from  each  of  the  following  prop- 
ositions to  the  next? 

(1)  No  knowledge  is  useless. 

(2)  No  useless  thing  is  knowledge. 
(8)  All  knowledge  is  not  useless. 

(4)  All  knowledge  is  useful. 

(5)  What  is  not  useful  is  not  knowledge. 

(6)  What  is  useless  is  not  knowledge 

(7)  No  knowledge  is  useless. 

6.  Give  the  logical  opposites  of  the  following  proposition,  and 

the  converse  of  its  contradictory : 

*  He  cannot  become  rich  who  will  not  labor." 

7.  Apply  negative  conception  to  the  proposition  "All  men  are 

fallible ; "  then  convert  and  show  that  the  result  is  the  con- 
trapoaitive  of  the  original. 

8.  Classify  the  pro{)Ositions  subjoined  into  the  four  following 

groups : 

a.  Those  which  can  be  inferred  from  (1), 

b.  Those  from  which  (I)  can  be  inferred. 

e.  Those  which  do  not  contradict  (1),  but  cannot  be  inferred 

from  it. 
d.  Those  which  contradict  (1). 

(1)  All  just  acts  are  expedient  acta. 

(2)  No  expedient  acts  are  unjust. 

(8)  No  just  acts  are  inexpedient 
(4)  All  inexpedient  acts  are  unjust. 
US)  Some  unjust  ac*s  are  inexpedient. 

(6)  No  expedient  acts  are  just 

(7)  Some  inexpedient  acts  are  ui^jnat 


PROPOSITIONS.  S9I 


(8)  All  expedient  acts  are  just. 

(9)  No  inexpedient  acts  are  j  ust. 

(10)  All  unjust  acts  are  inexpedient. 

(11)  Some  inexpedient  acts  are  just  acta. 

(12)  Some  expedient  acts  are  just. 

(13)  Some  just  acts  are  expedient. 

(14)  Some  unjust  acts  are  expedient. 


SECTION     IV. 

THE    LOGICAL    ANALYSIS    OF    SENTENCES. 

How  does  the  grammatical  predicate  differ  from  the  ^g^cai 

predicate  ? 
,  Distinguish  between  a  compound  and  a  complex  sentence ;  and 

between  co-ordinate  and  subordinate  propositions. 
,  Enumerate  the  grammatical  expressions  which  may  form 

(1)  A  subject.  (4)  An  object. 

(2)  An  attribute.  (5)  An  adverbial. 

(3)  A  predicate. 

,  Examine  the  following  sentences,  ascertain  which  are  com- 
pound  or  complex,  and  point  out  the  co-ordinate  or  subordi- 
nate propositions: 

(1)  Happy  is  the  man  that  findeth  wisdom,  and  the  man  that 

getteth  understanding. 

(2)  Heat,    being  motion,   can  be  converted  into  mechanica> 

force. 

(3)  Ceres,    Pallas,   Juno,   and  Vesta  are  minor    planets,    oi 

asteroids. 

(4)  Knowledge  comes,  but  wisdom  lingers. 

(5)  Fortune  often  sells  to  the  hasty  what  she  gives  to  thow 

who  wait. 

(6)  Thousands  at  His  bidding  speed. 
And  post  o'er  land  and  ocean  without  rest ; 
They  also  serve  who  only  stand  and  wait. 

(7)  Pride  that  dines  on  vanity,  sups  on  contempt 


293  BXEBGISES  AND    QUESTIONS. 

(8)  Nobody  can  be  healthful  without  exercise,  neither  natural 

body,  nor  politic. 

(9)  Nature  is  often  hidden,  somettmes  overcome,  seldom  ex* 

tinguished. 

(10)  It  is  impossible  to  love  and  be  wise. 

(11)  Though  gods  they  were,  as  men  they  died. 

(12)  He  that  is  not  industrious  envieth  him  that  is. 

(13)  Ye  are  my  friends,  if  ye  do  whatsoever  1  command  you. — 

John  XV.  14 

(14)  The  wisdom  that  is  from  above  is  first  pure,  then  peace- 

able, gentle,  and  easy  to  be  intreated,  full  of  mercy,  and 
good  fruits,  without  partiality,  and  without  hy[)ocrisy. — 
James  iii.  17. 
5.  Analyze  in  the  form  of  a  scheme  or  diagram  any  of  the  follow- 
ing sentences : — 

(1)  The  first  aphorism  of  Bacon's  Nomim  Organum,  on  p.  202. 

(2)  Some  judgments  are  merely  explanatory  of  their  subject, 

having  for  their  predicate,  a  conception  which  it  fairly 
implies,  to  all  who  know  and  can  define  its  nature. 

(3)  There  be  none  of  the  affections  which  have  been  noted  to 

fascinate  or  bewitch,  but  love  and  envy  ;  they  both  have 
vehement  wishes ;  they  frame  themselves  readily  into 
imaginations  and  suj^gestions  ;  and  they  come  easily  into 
the  eye,  e8i)ecially  upon  the  presence  of  the  objects,  which 
are  the  points  that  conduce  to  fascination,  if  any  such 
there  be. 

GENERAL    EXERCISES    ON    PROPOSITIONS. 

The  learner  is  desired  to  ascertain  the  logical  character  of  each 
of  the  following  propositions  ;  he  is  to  state  of  each  whether  it  is 
affirmative  or  negative,  universal,  particular,  singular  or  in- 
definite, pure  or  mo<la1,  exclusive  or  exceptive,  etc. ;  when 
irregularly  stated  he  is  to  reduce  the  projiosition  to  the  simple 
logical  order;  he  is  then  to  amvert  the  proposition,  and  to  draw 
immediate  inferences  from  it  by  any  process  which  may  be 
applicable. 

(1)  All  birds  are  feathered. 

(2)  No  reptiles  are  feathered. 


PROPOSITIONS.  293 

(8)  Pixed  stare  are  self-luminous. 

(4)  Perfect  happiness  is  impossible. 

(5)  Life  every  man  holds  dear. 

(6)  Every  mistake  is  not  a  proof  of  ignorance. 

(7)  Some  of  the  most  valuable  books  are  seldom  reaii 

(8)  He  jests  at  scars  who  never  felt  a  wound. 

(9)  Heated  metals  are  softened. 

(10)  Not  one  of  the  Greeks  at  Thermopylae  escaped. 

(11)  Few  are  acquainted  with  themselves. 

(12)  Whoso  loveth  instruction  loveth  knowledge. 

(13)  Nothing  is  harmless  that  is  mistaken  for  a  virtod. 

(14)  Some  of  our  muscles  act  without  volition. 

(15)  Metals  are  all  good  conductors  of  heat. 

(16)  Fame  is  no  plant  that  grows  on  mortal  soil. 

(17)  Only  the  brave  deserve  the  fair. 

(18)  No  one  is  free  who  doth  not  command  himself. 

(19)  Nothing  is  beautiful  except  truth. 

(20)  The  wicked  shall  fall  by  his  own  wickedness. 
f21)  Unsafe  are  all  things  unbecoming. 

(22)  There  is  no  excellent  beauty  that  hath  not  some  strange 

uess  in  the  proportion. 

(23)  It  is  a  poor  centre  of  a  man's  actions,  himself. 

(24)  Mercy  but  murders,  pardoning  those  that  kilL 

(25)  I  shall  not  all  die.     {Non  omnis  moiiar.) 

(26)  A  regiment  consists  of  two  battalions. 

(27)  'Tis  cruelty  to  load  a  falling  man. 

(28)  Every  mistake  is  not  culpable. 
(89)  Quadrupeds  are  vertebrate  animals. 

(30)  Not  many  of  the  metals  are  brittle. 

(31)  Many  are  the  deserving  men  who  are  unfortunate. 

(32)  Amalgams  are  alloys  of  mercury. 

(33)  One  kind  of  metal  at  least  is  liquid. 

(34)  Talents  are  often  misused. 

(35)  Some  parallelograms  have  their  adjoining  sides  equal 

(36)  Britain  is  an  island. 

(37)  Romulus  and  Remus  were  twins. 

(38)  A  man's  a  man. 

t89)  Heaven  is  all  mercy. 


294  EXERCISES  AND  QUESTIONS. 

(40)  Every  one  is  a  good  judge  of  his  own  interesta 

(41)  All  parallelograms  have  theiv  opposite  angles  eqoaL 

(42)  Familiarity  breeds  contempt. 

(43)  No  one  is  always  happy. 

(44)  Every  little  makes  a  mickla 


CHAPTER    III* 
SYLLOGISMS. 

SECTION    I. 

THE    LAWS    OF    THOUGHT 

1.  State  the  three  Fundamental  Laws  of  Thought,  and  apply  then 

to  the  following  notions : 

(1)  Matter,  organic,  inorganic. 

(2)  Undulations,  polarized,  nonpolarized. 
(8)  Figure,  rectilinear,  curvilinear. 

2.  Is  it  wrong  to  assert  that  an  animal  cannot  both  be  vertebrate 

and  invertebrate,  seeing  that  some  animals  are  vertebrate 

and  some  are  not  ? 
8.  Select  from  the  followng  such  terms  as  are  negatives  of  the 

others,  and  such  aT  aro   opposites : — Light,    plenum,  gain, 

heat,  decrease,  loss,  darkness,  cold,  increase,  vacuum. 
4.  How  is  Aristotle's  dictum  applicable  to  the  following  argfu- 

ments? 

(1)  Silver  is  a  good  conductor  of  electricity  ;  for  such  are  all 

the  metals. 

(2)  Comets  cannot  be  without  weight ;  for  they  are  composed 

of  matter,  which  is  not  without  weight 


8YLL0QISMB.  295 

SECTION    II. 
THE    RULES    OF   THE    SYLLOGISM. 

1  Distinguish  mediate  and  immediate  inference. 

8.  Define  syllogism,  and  state  with  what  it  is  synonymous. 

8.  What  are  the  six  principal  and  two  suhordinate  rules  of  th« 
syllogism  1 

4.  In  the  following  syllogisms  point  out  in  succession  the  con- 
clusion, the  middle  term,  the  major  term,  the  minor  term, 
the  major  premise  and  the  minor  premise,  observing  this 
precise  order. 

(1)  All  men  are  fallible ; 
All  kings  are  men ; 

Therefore  all  kings  are  fallible. 

(2)  Platinum  is  a  metal ; 

All  metals  combine  with  oxygen  ; 
Therefore  Platinum  combines  with  oxygen. 
(3)  Hottentots  are  capable  of  education ;   for  Hottentots  are 
men,  and  all  men  are  capable  of  education. 
6.  Explain  carefully  what  is  meant  by  non-distribution  of  the 
middle  term. 


SECTION     III. 

THE    MOODS    AND    FIGURES    OF   THE    SYLLOGISM. 

1.  Name  the  rules  of  the  syllogism  which  are  broken  by  any  ol 

the  following  moods,  no  regard  being  paid  to  figure : — 
AIA,  EEI,  lEA,  lOI,  IIA,  AEI, 

2.  Write  out  all  the  64  moods  of  the  syllogism  and  strike  out  th< 

53  invalid  ones. 

8.  Show  in  what  figures  the  following  premises  give  a  valid  con- 
clusion : — AA,  AI,  EA,  OA. 

4.  In  what  figures  are  lEO  and  EI 0  valid? 


296  gXERCISES   AND   QUESTIONS. 

6.  To  what  moods  do  the  following  valid  syllogisms  belong II 
Arrange  them  in  conect  logical  order. 
(1)  Some  Y's  are  Z's.  (2)  All  Z's  are  Y's. 

No  X's  are  Y's.  No  Y's  are  X'b. 

Some  Z's  are  not  X's  No  Z's  are  X'& 

(8)  No  fish  suckles  its  young ; 
The  whale  suckles  its  young ; 
Therefore  the  whale  is  no  fish. 

6.  Deduce  conclusions  from  the  following  premises ;  and  state  to 

what  inood  the  syllogism  belongs. 

(1)  Some  amphibious  animals  are  mammaliao. 
All  mammalian  animals  are  vertebrate. 

(2)  All  planets  are  heavenly  bodies. 
No  planets  are  self-luminous. 

(3)  Mammalian  animals  are  quadrupeds. 
No  birds  are  quadrupeds 

(4)  Ruminant  animals  are  not  prcdaceous. 
The  lion  is  predaceous. 

7.  Invent  examples  to  show  that  false  premises  may  give  true 

conclusions. 

8.  Supply  premises  to  the  following  conclusions. 

(1)  Some  logicians  are  not  good  reasoners. 

(2)  The  rings  of  Saturn  are  material  bodies. 

(3)  Party  government  exists  in  every  democracy. 

(4)  All  fixed  stars  obey  the  law  of  gravitation. 


SECTION     IV. 
THF    REDUCTION    OF    SYLLOGISMS. 

1.  State  and  wxplain  the  mnemonic  line.s  Barbara,  Celarent,  etc. 

8.  Construct  syllogisms  in  each  of  the  following  moods,  taking 
X,  Y,  Z,  for  the  major, middle,  and  minor  temis  resiHCtively 
and  show  how  to  reduce  them  to  the  first  figure: 
Cesare,  Festino,  Darapti,  Dutisi,  Fcrison,  Camenes,  Fesapo. 

8.  What  is  the  use  of  Reduction  ? 

1  Prove  that  the  following  premises  cannot  give  a   universa' 
conclusion — EI,  lA,  OA,  IE. 


SYLLOGISMS.  297 

5.  Prove  that  the  third  figure  must  have  an  affirmative  minoi 

premise,  and  a  particular  coiiclusion. 

6,  Reduce  the  moods  Cesare  and  Cameues  by  the  Indirect  method, 

or  Reductio  ad  Impossibile. 


SECTION     V. 
IRREGULAR    AND    COMPOUND    SYLLOGISMS. 

1.  Describe  the  meaning  of  each  of  the  terms — Enthymeme 

Prosyllogism,  Episjllogism,  Epicheirema,  Sorites. 

2.  Make  an  example  of  a  syllogism  in  which  there  are  two  pro- 

syllogisms. 
8.  Construct  a  sorites  of  four  premises  and  resolve  it  into  distinct 
syllogisms. 

4.  Wliat  are  the  rules  to  which  a  sorites  must  conform  ? 

5.  The  learner  is  requested  to  analyze  the  following  arguments, 

to  detect  those  which  are  false,  and  to  ascertain  tlie  rules  ni 
the  syllogism  which  tliey  break;  if  the  argument  appears 
valid  he  is  to  ascertain  the  figure  and  mood  to  which  it 
belongs,  to  state  it  in  correct  logical  form,  and  then  if  it  be 
in  an  imperfect  figure  to  prove  it  by  reduction  to  the  first 
figure.  The  first  six  of  the  examples  should  be  arraneed 
both  in  the  extensive  and  intensive  orders 
',!)  None  but  mortals  are  men. 

Monarchs  are  men. 

Therefore  monarchs  are  mortals. 
f2)  Personal  deformity  is  an  affliction  of  naiurt 

Disgrace  is  not  an  affliction  of  nature. 

Therefore  personal  deformity  is  not  disgrace. 

(3)  Some  statesmen  are  also  authors  ;  for  such  are  Mr.  Glad 

stone.  Lord  Derby,  Lord  Russell,  and  Sir  G,  C.  Lewis 

(4)  This  explosion  must  have  been  occasioned  by  gunpowder 

for  nothing  else  would  have  possessed  sufficient  force. 

(5)  Every  man  should  be  moderate ;  for  excess  will  cause  di* 

ease 
;U)  Blessed  are  the  meicilul ;  for  they  shall  obtain  mercy 


898  EXERCISES   AND   QUESnONS. 

(7)  Ab  almost  all  the  organs  of  the  body  have  a  known  om 

the  spleen  must  have  some  use. 

(8)  Cogito,  ergo  sum.    (I  think,  therefore  I  exist.) 

(9)  Some  speculative  men  are  unworthy  of  trust ;  for  they  an 

unwise,  and  no  unwise  man  can  be  trusted. 

(10)  No  idle  person   can  be  a  successful   writer  of  history 

therefore  Hume,  Macaulay,  Hallam  and  Qrote  must  have 
been  industrious. 

(11)  Who  spareth  the  rod,  hateth  his  child ;  the  parent  who 

loveth  his  child  therefore  spareth  not  the  rod. 

(12)  Comets  must  consist  of  heavy  matter ;  for  otherwise  they 

would  not  obey  the  law  of  gravitation. 

(18)  Lithium  is  an  element ;  for  it  is  an  alkali-producing  sab- 
stance,  which  is  a  metal,  which  is  an  element. 

(14)  Rational  beings  are  accountable  for  their  actions ;  brutea 
not  being  rational,  are  therefore  exempt  from  responsi- 
bility. 

(16)  A  singular  proposition  is  a  universal  one  ;  for  it  applies  to 

the  whole  of  its  subject. 
|16)  Whatever  tends  to  withdraw  the  mind  from  pursuits  ot 
a  low  nature  deserves  to  be  promoted ;  classical  learning 
does  this,  since  it  gives  us  a  taste  for  intellectual  enjoy* 
ments ;  therefore  it  deserves  to  be  promoted. 

(17)  Bacon  was  a  great  lawyer  and  statesman  ;  and  as  he  was 

also  a  philosopher,  we  may  infer  that  any  philosopher  may 
be  a  great  lawyer  and  statesman. 

(18)  Immoral  companions  should  be  avoided ;  but  some  im- 

moral companions  arc  intelligent  persons,  so  that  some 

intelligent  persons  should  be  avoided. 
(18)  Mathematical  study  undoubtedly  improves  the  reasoning 

powers ;  but,  as  the  study  of  logic  is  not  mathematical 

study,  we  may  infer  that  it  does  not  improve  the  reasoning 

powers. 
(20)  Every  candid  man  acknowledges  merit  in  a  rival ;  every 

learned  man  does  not  do  so ;  therefore  every  learned  man 

is  not  candid. 


8TLL0GISMS.  29S 


SECTION    VI. 

CONDITIONAL    ARGUMENTS. 

t  What  are  the  kinds  of  conditional  propositions,  and  by  what 
signs  can  you  recognize  them  ? 

2.  What  are  the  rules  of  the  hypothetical  syllogism? 

8.  To  what  categorical  fallacies  do  breaches  of  these  rules  cor- 
respond ? 

4.  Select  from  the  following  such  as  are  valid  arguments,  and 

reduce  them  to  the  categorical  form ;  explain  the  fallacious 
reasoning  in  the  others : 

(1)  Rain  has  fallen  if  the  ground  is  wet;  but  the  ground  is 

not  wet ;  therefore  rain  has  not  fallen. 
(8)  If  rain  has  fallen,  the  ground  is  wet;  but  rain  has  not 

fallen  ;  therefore  the  ground  is  not  wet. 
(8)  The  ground  is  wet,  if  rain  has  fallen ;  the  ground  is  wet ; 

therefore  rain  has  fallen. 
(4)  If  the  ground  is  wet,  rain  has  fallen ;  but  rain  has  fallen ; 

therefore  the  ground  is  wet. 
N.  B. — In  these  as  in  other  logical  examples  the  student  must 
argne  only  from  the  premises,  and  not  from  any  other  knowledge 
of  the  subject-matter. 

5.  Show  that  the  canons  of  syllogism  (pp.  108,  109)  may  be 

stated  indifferently  in  the  hypothetical  or  categorical  form. 
S.  State  the  following  in  the  form  of  a  Disjunctive  or  Dilemmatio 
argument,  and  name  the  kind  to  which  it  belongs. 
If  pain  is  severe  it  will  be  brief;  and  if  it  last  long  it  will  hf 
slight ;  therefore  it  is  to  be  patiently  borne. 


300  RXEECI?ES  AND   QUESTIONS 


CH&PTBH   IV. 

FALLACIES. 

1.  Classify  fallaciea 

8.  Explain  the  following  expressions  : 

A dicto  secundum  quid  ad  dictum  simpliciter ;  ignoratio  elenchi ; 

argumentum   ad   hominem ;  argumcntum    ad  populam ; 

petltio  principii ;  circulus  in  probando;  non  sequitur ;  post 

hoc  ergo  propter  hoc. 

8.  What  is  arguing  in  a  circle  ;  and  what  is  a  question-begging 

epithet? 

4.  What  diflFerences  of  meaning  may  be  produced  in  the  follow- 

ing sentence  by  varying  the  accent  ? 
"  Newton's  discovery  of  gravitation  is  not  generally  believed 
to  have  been  at  all  anticipated  by  several  philosophers  in 
Elngland  and  Holland." 

5.  Point  out  the  misinterpretations  to  which  the  following  sen- 

tences might  be  liable. 
(1)  He  went  to  London  and  then  to  Brighton  by  the  expresa 

train. 
(3)  Did  you  make  a  long  speech  at  the  meeting? 

(3)  How  much  is  five  times  seven  and  nine? 

8.  The  following  examples  consist  partly  of  true  and  partly  of 
false  arguments.  The  learner  is  requested  to  treat  them  a£ 
follows : 

(1)  If  the  example  is  not  in  a  simple  and  complete  logical  form 

to  complete  it  in  the  form  which  ap[)ear8  most  appropriate. 

(2)  To  ascertain  whether  it  is  a  valid  or  fallncious  argument. 
(8)  To  assign  the  exact  name  of  the  argument  or  fallacy  as  the 

case  may  be. 

(4)  If  a  categorical  syllogism,  to  reduce  it  to  the  first  figure. 
(6)  If  a  hypothetical  syllogism,  to  state  it  in  the  categoric»< 

form. 


FALLACIES.  301 

EXAMPLES   OF    ARGUMENTS. 

..  Elementary  gubstances  alone  are  metals.    Iron  is  a  metal 

therefore  it  is  an  elementary  substance. 
2.  No  Athenians  could  have  been  Helots  ;  for  all  the  Helots  wew 

slaves,  and  all  Athenians  were  free  men. 
8.  Aristotle  must  have  been  a  man  of  extraordinary  industry; 

for  only  such  a  man  could  have  produced  his  works. 
1  Nothing  is  better  than  wisdom ;  dry  bread  is  better  than 

nothing  ;  therefore  dry  bread  is  better  than  wisdom. 

5.  Pitt  was  not  a  great  and  useful  minister ;  for  though  lie  would 

have  been  so  had  lie  carried  out  Adam  Smith's  doctrines  of 
Free  Trade,  he  did  not  carry  out  those  doctrines. 

6.  Only  the  virtuous  are  truly  noble  ;  some  who  are  called  noble 

are  not  virtuous;  therefore  some  who  are  called  noble  are 
not  truly  noble. 

7.  Ireland  is  idle  and  therefore  starves ;  she  starves,  and  there. 

fore  rebels. 

8.  No  designing  person  ought  to  be  trusted :  engravers  are  by 

profession  designers ;  therefore  they  ought  not  to  hi  trusted. 
0.  Logic  as  it  was  cultivated  by  the  schoolmen  proved  a  fruitless 
study ;  therefore  Logic  as  it  is  cultivated  at  the  present  day 
must  be  a  fruitless  study  likewise, 

10.  Is  a  stone  a  body?  Yes.  Then  is  not  an  animal  a  bodyt 
Yes.  Are  you  an  animal  ?  1  think  so.  Ergo,  you  are  a 
stone,  being  a  body. — Lucia  n, 

11.  If  ye  were  Abraham's  children,  ye  would  do  the  works  ol 

Abraham. — John  viii.  39. 

12.  He  that  is  of  God  heareth  God's  words :  ye  therefore  hear 
them  not,  because  ye  are  not  of  God. — John  viii.  47. 

13.  Mahomet  was  a  veise  lawgiver ;  for  he  studied  the  character 
of  his  people. 

14.  Every  one  desires  virtue,  because  every  one  desires  happi- 
ness. 

15.  His  imbecility  of  character  might  have  been  inferred  from 
his  proneness  to  favorites ;  for  all  weak  princes  have  thla 
failing. — De  Morgan. 

16    He  is  brave  who  Tonquers  his  passions ;  he  who  resists  temp 


S02  EXERCISES   AND   QUESTION'S. 

tation  conquers  his  passions ;  so  that  he  who  resists  temp 

tation  is  brave. 
17.  Suicide  is  not  always  to  be  condemned ;  for  it  is  but  volun- 
tary death,  and  this  has  been  gladly  embraced  by  many  ol 

the  greatest  heroes  of  antiquity. 
J8.  Since  all  metals  are  elements,  the  most  rare  of  all  the  metalr 

must  be  the  most  rare  of  all  the  elements. 
19.  The  express  train  alone  does  not  stop  at  this  station ;  and  aa 

the  last  train  did  not  stop  it  must  have  been  the  express 

train. 
80.  Peel's  remission  of  taxes  was  beneficial ;  the  taxes  remitted 

by  Peel  were  indirect ;  therefore  the  remission  of  indirect 

taxes  is  beneficial. 
31.  Books  are  a  source  both  of  instruction  and  amusement ;  u 

table  of  logarithms  is  a  book  ;  therefore  it  is  a  source  both  of 

instruction  and  amusement. 
33.  All  desires  are  not  blameable ;  all  desires  are  liable  to  ex- 
cess ;  therefore  some  things  liable  to  excess  are  not  blameable. 
23.  Whosoever  intentionally  kills  another  should  suffer  death ;  a 

soldier,  therefore,  who  kills  his  enemy  should  suffer  death. 

84.  Projectors  are  unfit  to  be  trusted ;  this  man  has  formed  a 

project ;  therefore  he  is  unfit  to  be  trusted, 

85.  Few  towns  in  the  United  Kingdom  have  more  than  800,000 

inhabitants;  and  as  all  such  towns  ought  to  be  represented 
by  three  members  in  Parliament,  it  is  evident  that  few 
towns  ought  to  have  three  representatives. 

80.  All  the  works  of  Shakspeare  cannot  be  read  in  a  day ;  there- 
fore  the  play  of  Hamlet,  being  one  of  the  works  of  Shak- 
speare, cannot  be  read  in  a  day. 

i/7.  In  moral  matters  we  cannot  stand  still ;  therefore  he  who 
does  not  go  forward  is  sure  to  fall  behind. 

28.  The  people  of  the  country  are  suffering  from  famine ;  and  at 
you  are  one  of  the  people  of  the  country  you  must  be  suffer- 
ing from  famine. 

28.  Those  substances  which  are  lighter  than  water  can  float  upoa 
it;  those  metals  which  can  float  upon  it  are  potassium, 
sodium,  lithium,  etc.;  therefore  potassium,  sodium,  lithium 
titc..  are  liirhter  than  water. 


FALLACIES.  803 

30.  The  laws  of  nature  must  be  ascertained  by  Deduction,  Tm- 

duction  or  Induction ;  but  the  former  two  are  insufficient  for 
the  purpose  ;  therefore  the  laws  of  nature  must  be  ascertained 
by  Induction. 

31.  A  successful  author  must  be  either  very  industrious  or  very 

talentefi ;  Gibbon  was  very  industrious,  therefore  he  waa 
not  very  talented. 
33.  Tou  are  not  what  I  am  ;  I  am  a  man  ;  therefore  you  are  not  a 
man. 

33.  The  liolder  of  some  shares  in  a  lottery  is  sure  to  gain  a 

prize ;  and  as  I  am  the  holder  of  some  shares  in  a  lottery  I 
am  sure  to  gain  a  prize. 

34.  Gold  and  silver  are  wealth ;  and  therefore  the  diminution  of 

the  gold  and  silver  in  the  country  by  exportation  is  the 
diminution  of  the  wealth  of  the  country. 

85.  Over-credulous  persons  ought  never  to  be  believed ;  and  as 

the  Ancient  Historians  were  in  many  instances  over-credu 
lous  they  ought  never  to  be  believed. 

86.  Some  mineral  compounds  are  not  decomposed  by  heat ;  all 

organic  substai^ces  are  decomposed  by  heat;  therefore  no 
organic  substances  are  mineral  compounds. 

87.  Whatever  schools    exclude    religion   are  irreligious ;    Non- 

sectarian  schools  do  Qot  allow  the  teaching  of  religious 
creeds  ;  therefore  they  are  irreligious. 

38.  Night  must  be  the  cause  of  day  ;  for  it  invariably  precedes  it. 

39.  The  ancient  Greeks  produced  the  greatest  master-pieces  of 

eloquence  and  philosophy  ;  tbe  Lacedaemonians  were  ancient 
Greeks ;  therefore  they  produced  the  greatest  master-pieces 
of  eloquence  and  philosophy. 

40.  All  presuming  men  are  contemptible;  this  man,  therefore,  is 

"/ontemptible ;  for  he  presumes  to  believe  his  opinions  are 
correct. 

41.  If  a  substance  is  solid  it  possesses  elasticity,  and  so  also  it  does 

if  it  be  liquid  or  gaseous  ;  but  all  substances  are  either  solid, 
liquid  or  gaseous  ;  therefore  all  substances  possess  elasticity. 
13  If  Parr's  life  pills  are  of  any  value  those  who  take  them  will 
improve  in  health  ;  now  my  friend  who  has  been  taking 
them  has  improved  in  health  ;  therefore  they  are  of  valu*- 


304  EXERCISES  AND   QUESTIONS. 

43.  He  who  calls  you  a  man  speaks  truly ;  he  who  calls  you  e 

fool  calls  you  a  man ;   therefore  he  who  calls  you  a  fool 
speaks  truly. 

44.  Who  is  most  hungry  eats  most ;  who  eats  least  is  most 

hungry  ;  tlierefore  who  eats  least  eats  most. 
46.   What  produces  intoxication  should  be  prohibited;  the  use  of 
spirituous  liquors  causes  intoxication;  tlierefore  the  use  ol 
spirituous  liquors  shf)uld  be  prohibited. 

46.  What  we  eat  grew  in  the  fields  ;  loaves  of  bread  are  what  w« 

eat ;  tlierefore  loaves  of  bread  grew  in  the  fields. 

47.  If  light  consisted  of  material  particles  it  would  possess  mo- 

mentum ;  it  cannot  therefore  consist  of  material  particles, 
for  it  does  not  ix)8ses8  momentum. 

48.  Everything  is  allowed  by  law  which  is  morally  right ;  in- 

dulgence in  pleasures  la  allowed  by  law ;  therefore  indul 
gence  in  pleasures  is  morally  right. 

49.  All  the  trees  in  the  park  make  a  thick  shade ;  this  isone  of 

them,  therefore  this  tree  makes  a  thick  shade. 

BO.  All  visible  bodies  shine  by  their  own  or  by  reflected  light. 
The  moon  does  not  shine  by  its  own,  therefore  it  shines  by 
reflected  light ;  but  the  sun  shines  by  its  own  light,  there- 
fore it  cannot  shine  by  reflected  light. 

51.  Honesty  deserves  reward;  and  a  negro  is  a  fellow -creature; 
therefore,  an  honest  negro  is  a  fellow-creature  deserving  ol 
reward. 

53.  Nearly  all  the  satellites  revolve  round  their  planets  from 
west  to  east;  the  moon  is  a  satellite;  therefore  it  revolves 
round  its  planet  from  west  to  east. 

53.  Italy  is  a  Catholic  country  and  abounds  in  beggars;  France 

is  also  a  Catholic  country,  and  therefore  abounds  in  beg- 
gars. 

54.  Every  law  is  either  useless  or  it  occasions  hurt  to  some  per- 

son ;  now  a  law  that  is  useless  ought  to  be  abolished  ;  and 

so  ought  every  law  that  occasions  hurt ;   therefore  every 

law  ought  to  be  alxilished. 
66.  The  end  of  a  thing  is  its  perfection  ;  death  is  the  end  of  life 

therefore  death  is  the  perfection  of  life. 
66.  When  we  hear  that  all  the  righteous  people  are  happy,  it  it 


FALLACIES.  SOfi 

hard  to  avoid  exclaiming,  Wliat  i  are  all  the  unhappy  per- 
sons we  see  to  be  thought  unrighteous  ? 

57.  I  am  offered  a  sum  of  money  to  tSt-st  this  person  in  gaining 
the  oflBce  he  desires  ;  to  assist  a  peK-on  is  to  do  him  good, 
and  no  rule  of  morality  forbids  the  doing  of  good  ;  therefore 
no  rule  of  morality  fori^ids  me  to  receive  the  sum  of  money 
for  assisting  the  pereon. 

68.  Ruminant  animals  are  those  which  have  cloven  feet,  and 
they  usually  have  horns  ;  the  extinct  animal  which  left  this 
footprint  had  a  cloven  foot ;  tlierefore  it  was  a  ruminant 
animal  and  had  horns.  Again,  as  no  beasts  of  prey  are 
ruminant  animals  it  cannot  have  been  a  beast  of  prey. 

59.  We  must  either  gratify  our  vicious  propensities,  or  resist 

them ;  the  former  course  will  involve  us  in  sin  and  misery  ; 
the  latter  requires  self-denial;  therefore  we  must  either  fall 
into  sin  and  misery  or  practise  self-deniaL 

60.  The  stonemasons  are  benefited  by  the  masons'  union  ;  the 

bricklayers  by  the  bricklayers'  union ;  the  hatmakers  by  the 
hatmakers'  union ;  in  short,  every  trade  by  its  own  union  : 
therefore  it  is  evident  that  if  all  workmen  had  unions  all 
workmen  would  be  benefited  thereby. 

61.  Every  moral  aim  requires  the  rational  means  of  attaining  it ; 

these  means  are  the  establishment  of  laws ;  and  as  happiness 
is  the  moral  aim  of  man  it  follows  that  the  attainment  of 
happiness  requires  the  establishment  of  laws. 

62.  He  that  can  swim  needs  not  despair  to  fly;  for  to  swim  is  to 

fly  in  a  grosser  fluid,  and  to  fly  is  to  swim  in  a  subtler. 

63.  The   Eelvetii,   if   they  went    thrr^ugh   the  country  of   the 

Sequani,  were  sure  to  meet  with  yarious  difficulties  ;  and  if 
they  went  through  the  Roman  p.*ovince,  they  were  exposed 
to  the  danger  of  opposition  from  Cajsar ;  but  they  were 
obliged  to  go  one  way  or  the  other ;  therefore  they  were 
either  sure  of  meeting  with  various  difliculties,  or  of  being 
exposed  to  the  danger  of  opposition  from  Caesar. — De  Belle 
Gnllico,  lib.  i.  6. 

64.  Riches  are  for  spending,  and  sjiending  for  honor  and  good 

actions;  therefore  extraordinary  expense  must  oe  limited 
by  the  worth  of  the  occasion. — Bacon. 


306  BXERCrSES  AND  QUBSHONB. 

G5.  If  liglit  is  not  refracted  near  the  surface  of  the  moon,  ther« 
cannot  be  any  twilight ;  but  if  the  moon  has  no  atmosphere 
light  is  not  refracted  near  its  surface  ;  therefore.if  the  moon 
has  no  atmosphere  there  cannot  be  any  twilight. 

36.  The  preservation  of  society  requires  exchange  ;  whatever  re- 
quires exchange  requires  equitable  valuation  of  property; 
tliis  requires  the  adoption  of  a  common  measure  ;  hence  the 
preservation  of  society  requires  the  adoption  of  a  common 
measure. 

67  The  Several  species  of  brutes  beinpr  created  to  prey  upon  one 
another  proves  that  the  human  species  were  intended  to 
prey  upon  them. 

68.  The  more  correct  the  logic,  the  more  certainly  the  conclusion 

will  be  wrong  if  the  premises  are  false.  Therefore  where 
the  premises  are  whoUy  uncertain,  the  best  logician  is  the 
least  safe  guide. 

69.  If  our  rulers  could  be  trusted  always  to  look  to  the  best 

interests  of  their  subjects,  monarchy  would  be  the  best  form 
of  government ;  but  they  cannot  be  trusted ;  therefore 
monarchy  is  not  the  best  form  of  government. 

70.  If  men  were  prudent,  they  would  act  morally  for  their  own 

good ;  if  benevolent,  for  the  good  of  others.  But  many  men 
will  not  act  morally,  either  for  their  own  good,  or  that  ot 
others  ;  such  men,  therefore,  are  not  prudent  or  benevolent. 

71.  He  who  bears  arms  at  the  command  of  the  magistrate  docs 

what  is  lawful  for  a  Christian  ;  the  Swiss  in  the  French  ser- 
vice, and  the  British  in  the  American  service,  bore  arms  at 
the  command  of  the  magistrate ;  therefore  they  did  what 
was  lawful  for  a  Christian. —  Whately. 

72.  A  man  that  hath  no  virtue  in  himself  ever  envieth  virtue  in 

others ;  for  men's  minds  will  either  feed  upon  their  own 
good  or  upon  others'  evil  ;  and  who  wanteth  the  one  will 
prey  upon  the  other. — Bncon, 

?3.  The  object  of  war  is  durable  peace  ;  therefore  soldiers  are  the 
best  peace-makers. 

74  Confidence  in  promises  is  essential  to  the  intercourse  of 
human  life  ;  for  without  it  the  greatest  part  of  our  conduct 
would  proceed  upon  chance.     But  there  could  be  no  confi 


FALLACIES.  80? 

deoce  In  promises,  if  men  were  not  obliged  to  perform  them 
the  obligation,  tlierefore,  to  perform  promises  is  essentia]  to 
the  same  ends  and  in  the  same  degree. 
78i  If  the  majority  of  those  who  use  public-houses  are  prepared 
to  close  them,  legislation  is  unnecessary ;  but  if  they  are  not 
prepared  for  such  a  measure,  then  to  force  it  on  them  by  out- 
side pressure  is  both  dangerous  and  unjust. 

76.  He  who  believes  himself  to  be  always  in  the  right  in  \\ia 

opinion,  lays  claim  to  infallibility  ;  you  always  believe  your, 
self  to  be  in  the  right  in  your  opinion ;  therefore  you  lay 
claim  to  infallibility. —  Wliately. 

77.  If  we  never  find  skins  except  as  the  teguments  of  animals,  we 

may  safely  conclude  that  animals  cannot  exist  without  skina 
If  color  cannot  exist  by  itself,  it  follows  that  neither  can  any 
thing  that  is  colored  exist  without  color.  So,  if  language 
without  thought  is  unreal,  thought  without  language  must 
also  be  so. 

78.  No  soldiers  should  be  brought  into  the  field  who  are  not  well 

qualified  to  perform  their  part ;  none  but  veterans  are  well 
qualified  to  perform  their  part ;  therefore  none  but  veterans 
should  be  brought  into  the  field. —  Whately. 

79.  The  minimum  visibile  is  the  least  magnitude  which  can  be 

seen ;  no  part  of  it  alone  is  visible,  and  yet  all  parts  of  it 
must  aflfect  the  mind  in  order  that  it  may  be  visible ;  there- 
fore, every  part  of  it  must  affect  the  mind  without  being 
visible. 

80.  The  scarlet  poppy  belongs  to  the  genus  Papaver,  of  the 

natural  order  Papaveraceae  ;  which  again  is  part  of  the  sub. 
class  Thalamiflorae,  belonging  to  the  great  class  of  Dicotyle- 
dons. Hence  the  scarlet  poppy  is  one  of  the  Dicotyledons. 
81  Improbable  events  happen  almost  every  day;  but  what 
happens  almost  every  day  is  a  very  probable  event ;  there. 
fore  improbable  events  are  very  probable  events. —  Whately 


808  EXEBGISES  AND  QUESTIOK& 

CHAPTSH   Y. 
INDUCTION. 


SECTION    I. 

THE    INDUCTIVE    SYLLOGISM. 

1,  How  do  Induction  and  Deduction  differ? 

2.  Find  an  instance  of  reasoning  in  Traduction. 
8.  Distinguisli  Perfi^ct  and  Imixjrfect  Induction. 

4.  How  does  Mr.  Mill  define  Induction,  and  what  is  hJs  opinion 

of  Imperfect  Induction? 
6.  What  is  the  use  of  Perfect  Induction  ? 
6.  Construct   some    instances  of  the  inductive  syllogism,  and 

show  that  they  may  be  thrown  into  a  disjunctive  fonu. 


SECTION    II. 
THE   FORMS   OF   INDUCTION. 

L  From  what  circumstance  arise  the  certainty  and  generality  of 
reasoning  in  geometry  ? 

i.  Rnd  other  instances  of  certain  and  general  reasoning  concern- 
ing the  properties  of  numl)er8. 

3.  Why  are  inductive  conclusions  concerning  prime  numbers  un- 
certain and  not  general  ? 

4  Why  is  a  single  instance  sometimes  sufficient  to  warrant  a 
universal  conclusion,  while  in  other  cases  the  greatest  pos- 
sible number  of  concurring  instances,  without  any  exception, 
is  not  sufficient  to  warrant  such  a  conclusion? 

fi.  What  are  the  strict  and  ordinary  meanings  of  the  woi^ 
analogy? 


METHOD.  809 

CHAPTER   YI. 
METHOD. 


SECTION    I. 

INDUCTIVE    METHOD. 


1.  What  Is  th«  false  method  of  Sdence  against  which  Bacon  pro 

tested? 

8.  Explain  tue  exact  meau'ng  of  Bacon's  assertions,  that  man  is 
the  Servant  and  Interpreter  of  Nature,  and  that  Knowledge 
is  Power. 

3.  How  does  experiment  differ  from  observation? 

4  Classify  the  sciences  according  as  they  employ  passive  obser- 
vation, experiment,  or  both. 

5.  Name  the  chief  points  in  which  experiment  is  superior  to 

mere  observation. 

6.  What  is  the  principal  precaution  needful  in  observation  ? 

7.  Explain  how  it  is  iwssible   to  anticipate  nature  and  yet 

establish  all  conclusions  upon  the  results  of  experience, 

8.  Define  exactly  what  is  meant  by  a  cause  of  an  event,  and 

distinguish  cause,  occasion,  antecedent. 

9.  Point  out  all  the  causes  concerned  in  the  foUo^ng  ph«v 

nomena : 

(1)  The  burning  of  a  fire. 

(2)  The  ordinary  growth  of  vegetables. 

(3)  The  cracking  of  a  glass  by  hot  water. 

10.  State  and  explain  in  your  own  words  Mr.  Mill's  first  threa 

Canons  of  Inductive  Method. 

11.  Point  out  exactly  how  the  Joint  Method  differs  from  th* 

simple  Method  of  Difference. 
13.  Give  some  instances  of  simple  experiments  fulfilling  com- 
pletely the  conditions  of  the  Method  of  Difference. 


810  EXERCISES  AND   QUESTIONS. 

18.   What  can  jou  infer  from  the  following  instances? 
Antecedents.  Consequents. 

ABDE stqp 

BOB qsr 

BFG vqu 

ABE. Up 

HK. QcqiB 

ABFQ .pguv 

ABE. 4.....pqt. 


SECTION    11  = 
DEDUCTIVE    METHOD. 


1.  Define  each  of  Lhe  five  predicables. 

2.  In  what  sense  may  we  say  that  the  genus  is  part  of  the 

species,  and  in  what  sense  that  the  species  is  part  of  th« 
ginus  ? 

8.  Select  from  the  terms  in  the  sixth  question  of  Chapter  I, 
Section  III,  p.  287,  such  as  are  genera,  species,  higliest 
genera,  or  lowest  species  of  other  terms. 

4.  Explain  the  expressions  sui  generis,  liomogeneous,  hetero- 
geneous, summum  genus,  infima  sjiecies,  tree  of  Porphyry. 

6.  Name  a  property    and    accident  of    each  of  the  following 

classes : — Circle,   Planet,  Bird.  Member  of  Parliament,  Ru- 
minant Animal. 
8.  What  are  the  rules  of  correct  logical  division? 

7.  The  first  name  in  each  of  the  following  series  of  terms  is  that 

of  a  class  which  you  are  to  divide  and  subdivide  so  as  to 
include  all  the  subjoined  minor  classes  in  accordance  with 
the  laws  of  division. 

(1)  People.  (2)  Triangle.  (8)  Reasoning. 

Laity  Equiangular  Induction  (Imperfect; 

Aliens  Isosceles  Deduction 

Naturalized  Subjects  Right  angled  Mediate  Inference 


METHOD. 


811 


0)  People. 

Peers 

Natural-bora  Subjects 

Clergy 

Baronets 

Com  moos 


(2)  Triangle. 

Scalene 

Obtuse-augled 


(3)  Reasoning. 
Induction 

Hypothetical  Byllogisia 
Disjunctive  Syllogism 


8  Divide  any  of  the  following  classes : — Governments,  Science* 

Logical  terms,  Propositions. 

9  Of  what  does  a  logical  definition  consist? 
10.  What  are  the  rules  of  correct  definition  ? 

U.  What  rules  do  the  following  definitions  break  ? 

(1)  Life  is  the  sum  of  the  vital  functions. 

(2)  Genus  is  the  material  part  of  the  species. 

(3)  Illative  conversion  is  that  in  which  the  truth  of  the  con 

verse  can  be  inferred  from  that  of  the  convertend. 

(4)  Mineral  substances  are  those  which  have  not  been  pro- 

duced by  the  powers  of  vegetable  or  animal  life. 

(5)  An  equilateral  triangle  is  a  triangle  whose  sides  and  angles 

are  respectively  equal. 

(6)  An  acute-angled  triangle  is  one  which  has  an  acute  angle. 

12.  Define  classification,  and  give  the  derivation  of  the  word. 

13.  What  do  you  mean  by  important  cliaracters  in  classification? 

14.  State  the  requisites  of  a  good  classification. 

15.  What  are  the  three  purposes  for  which  we  use  language? 

16.  What  are  the  essentials  of  language  as  an  instrument  ol 

scientific  record  ? 


SECTION     III. 

COMPLETE     METHOD. 

1.  Define  Empirical  Law,  and  find  a  few  additional  instances  of 

such  laws. 
3.  What  are  the  three  steps  of  the  Complete  Method  ? 
8.  Trace  some  of  the  successive  steps  in  the  progress  of  the 


312  EXERCISES  AND  QUESTIONS. 

theory  of  gravitation,  showing  that  it  was  established  hf 
this  method. 
4  What  do  you  mean  by  the  explanation  of  a  fact? 

6.  State  the  tliree  ways  in  which  a  law  of  nature  may  be  ex- 

plained,  and  suggest  some  additional  instances  of  each  case. 
8.  State  the  five  rules  of  metliod  given  in  the  Port  Royal  Logic 

7.  Explain  Descartes'  rules  for  the  attainment  of  trutlu 


CHAPTER    YII. 
RECENT    LOGICAL    VIEWS. 


SECTION     I. 
THE  QUANTIFICATION   OF  THE  PREDICATE. 

1.  What  does  the  quantification  of  the  predicate  mean  ? 

2.  Assign  to  each  of  the  following  propositions  its  proper  sym 

bol,  and  the  symbol  of  its  converse  : 

(1)  Knowledge  is  power. 

(2)  Some  rectangles  are  all  squares. 

(8)  Only  the  honest  u  tiraately  prosper. 
(4)  Princes  have  but  their  titles  for  their  glories. 
(6)  In  man  there  is  nothing?  great  but  mind. 
(6)  The  end  of  philosoiihy  is  the  detection  of  unity. 
8.  Draw  all  the  contrapositive  propositions  and  immediate  infer 
ences  you  can  from  the  following  propositions: — 

(1)  London  is  a  great  city. 

(2)  London  is  the  capital  of  England. 

(3)  All  runiiiiaut  animals  are  all  cloven-footed  animals. 
^4)  Some  members  of  parliament  are  all  the  ministers. 

i.  Write  out  in  Hamilton's  notation  the  moods  Baroko,  Darapti, 
Felapton,  Bokardo. 


RECEirr  LOaiCAL  VIEWS.  81ft 

SECTION   II. 

BOOLE'S  SYSTEM   OF  LOGIC. 

1.  Apply  tliis  system  of  inference  to  prove  the  eyllogisms  on 

p.  130,  in  Cesare,  and  Camestres. 

2.  Show  that  if  all  A'a  are  not  B'a,  then  no  B's  are  A'a ;  and 

that  if  all  ^.'s  are  all  B'a,  then  all  not  A'a  are  all  not  B'e. 
8.  Develop  the  term  substance,  as  regards  the  terms  vegetable, 

animal,  organic ;  then  select  the  combinations  which  agree 

with  these  premises : 

*'  What  is  vegetable  is  not  animal  but  is  organic ;  what 
is  animal  is  organic." 
4.  Test  the  validity  of  this  argument :  "Good  always  triumphs, 

and  vice  always  fails ;  therefore  the  victor  cannot  be  wrong, 

nor  the  vanquished  right.' 
6.  It  is  known  of  a  certain  class  of  things  that — 

(1)  Where  the  quality  A  is,  B  is  not. 

(2)  Where  B  is,  and  only  where  B  is,  G  and  D  are. 

What  can  we  infer  from  these  premises  of  the  class  oi 
things  in  which  A  is  not  present  but  G  is  present  ? 
%.  If  all  ^'s  are  B'a  ;  all  B'a  are  G'a ;  all  G'a  are  B'a;  show  that 
all  A'a  are  B'a,  and  that  all  not  B'b  are  not  A'a. 


AND    GLOSSARY. 


Note. — In  this  Index  and  Glossary,  besides  references  to  all 
the  important  topics  treated  of  in  the  volume,  may  be  found  brief 
definitions  of  all  the  logical  and  philosophical  terms  employed, 
and  short  sketches  of  the  lives  of  the  principal  writers  men- 
tioned. 


Abacus,  the  logical,  285. 

Abscissio  Infiniti  (the  cutting 
off  of  the  infinite  or  negative 
part),  the  process  by  wliich 
we  determine  the  position  of 
an  object  in  a  system  of 
classes,  by  successive  com- 
parison and  rejection  of  those 
classes  to  which  it  does  not 
belong. 

Absolute  terms,  i.e.,  non-rela- 
tive terms,  27 ;  sometimes 
used  as  name  of  non-conno- 
tative  terms,  4.5. 

Abstract  terms,  22,  45. 

Accent,  fallacy  of,  167. 

Accident,  fallacy  of,  169 ;  the 
predicable,  232. 

Accidental  definition  is  a  defi- 
nition which  assigns  the  pro- 
perties of  a  species,   or  the 


accidents  of  an  individual ;  it 

is  more   commonly   called  a 

Description. 
Added  determinants,  inference 

by,  91. 
Adequate  knovvledge,  59. 
A  dicto  secundum  quid,  etc., 

fallacy  of,  169. 
Adjectives,  38. 
Adverbials,  99. 
Affirmative  propositions,  67. 
Algebraic  reasoning,  61,  190. 
Ambiguity  of  all,  22 ;  of  8o7ne, 

84 ;  of  many  old  terms,  34. 
Ambiguous  middle  term,  118, 

163. 
Amphibology,  fallacy  of,  164 
Ampliative  propositions,  73. 
Analogue,  a  thing   analogous 

to  some  other  thing. 
Analysis,  method  of,  199. 


INDEX  AND  GLOSSARY. 


816 


Analogy,  the  cause  of  ambi- 
guity, 38  ;  reas^'^ning  by,  167, 
168. 

Analytics  (rd  'kvaXvTiKu),  the 
title  given  in  the  second  cen- 
tury to  portions  of  the  Orga- 
non,  or  Logical  Treatises  of 
Aristotle ;  they  were  distin- 
guished as  the  Prior  and  Pos- 
terior Analytics. 

Analytic  syllogism,  a  syllo- 
gism in  which  the  conclusion 
is  placed  first,  the  premises 
following  as  the  reasons.  See 
Synthetic  Syllogism  ;  the  dis- 
tinction is  unimportant. 

Antecedent,  of  a  hypothetical 
proposition,  150 ;  of  an  event, 
214. 

Anticipation  of  nature,  202. 

Antinomy  {uvrl,  against ;  vo/xci, 
law),  the  opposition  of  one 
law  or  rule  to  another.    Kant. 

A  posteriori  knowledge,  200. 

A  priori  knowledge,  200. 

Arbor  Porphyriana,  see  Tree 
of  Porphyry. 

Argument,  (Latin,  argus,  from 
upyd(,  clear,  manifest,)  the 
process  of  reasoning,  the 
showing  or  proving  that 
which  is  doubtful  by  that 
which  is  known.  See  Infer- 
ence. The  middle  term  of  a 
syllogism  is  sometimes  called 
specially  the  argument. 

Arguraentum  a  fortiori,  an 
argument  in  which  we  prove 


that  the  case  in  qaestion  Li 
more  strong  or  probable  than 
one  already  conceded  to  be 
suflBciently  so. 

Argumentum  ad  hominem 
172. 

Argumentum  ad  judicium,  an 
appeal  to  the  common  sense 
of  mankind. 

Argumentum  ad  ignorantiam, 
an  argument  founded  on  the 
ignorance  of  adversaries. 

Argumentum  ad  populum,  172. 

Argumentum  ad  verecundiam, 
an  appeal  to  our  respect  for 
some  great  authority. 

Argumentum  ex  concesso,  a 
proof  derived  from  a  proposi- 
tion already  conceded. 

Aristotle,  one  of  the  greatest 
philosophers  of  antiquity  (B.C. 
384-322),  a  pupil  of  Plato,  and 
preceptor  of  Alexander  the 
Great.  Aristotle  wrote  fam- 
ous works  on  Metaphysics, 
Physics,  Logic  and  Psychol- 
ogy. His  Logic  has  furnished 
the  foundations  of  the  science 
treated  under  that  name  since 
his  day,  and  he  may  justly  be 
regarded  as  the  father  of  that 
science.  His  doctrines  were 
accepted  by  the  sclioolmen  of 
the  European  Universities 
and,  though  strangely  mis- 
understood by  them,  were  re- 
garded as  having  an  almost 
divine  authority. 


816 


IKDEX  AND  GLOSSABT. 


Aristotle's  Dicta,  111. 

Assertion,  {ad,  to ;  sero,  to 
join,)  a  statement  or  proposi- 
tion, afSrmative  or  negative. 

Association  of  ideas,  {associo, 
to  accompany ;  aocius,  a  com- 
panion,) the  natural  connec- 
tion existing  in  the  mind  be- 
tween impressions  which  liave 
previously  coexisted,  or  which 
are  similar.  Any  idea  tends 
to  bring  into  the  mind  its 
associated  ideas,  in  accordance 
with  the  two  g^eat  laws  of 
association,  the  Law  of  Con- 
tiguity, and  the  Law  of 
Similarity. 

Assumption,  {asmmo,  to  take 
for  granted,)  any  proposition 
taken  as  the  basis  of  argu- 
ment ;  in  a  special  sense,  the 
minor  premise  of  a  categori- 
cal syllogism. 

Attribute,  (attnbuo,  to  give  or 
ascribe  to,)  a  quality  or  cir- 
cumstance which  may  be 
affirmed  (or  denied)  of  a 
thing ;  opposed  to  Substance, 
which  see. 

Attribute  in  grammar,  98. 

Attributive  term,  i.e.,  Connota- 
tite  term.  43. 

Axiom,  definition  of,  110. 

Baconian  method,  251. 
Barbara,  Ola  rent,  etc.,  134. 
Begging  the  Question,  173. 
Belief,  assent  to  a  proposition. 


admitting  of  any  degree  of 
strength,  from  the  slightest 
probabi  lity  to  the  fullest  cer- 
tainty ;  see  PrubaJinlity. 

Bentham,  George,  new  system 
of  Logic,  268. 

Boole,  George,  his  system  of 
Logic,  272. 

Canons  of  syllogism,  108,  9; 
Hamilton's  supreme  Canon. 

Canons  of  Mill's  Inductive 
Methods,  215. 

Categorematic  words,  19. 

Categorical  propositions,  67. 

Categories,  the  aumma  ge/iera, 
or  most  extensive  classes  into 
which  things  can  be  distrib 
utod;  they  are  ten  in  num. 
ber,  as  follows : 

Ovaia,  Substance;  no<T5v, 
Quantity ;  Uolov,  Quality 
ripov  Tc,  Relation;  Tloielv, 
Action;  Ruaxeiv,  Passion,  or 
suffering ;  Tlov,  Place  ;  Hare, 
Time;  Kelaftai,  Position; 
'Exeiv,  Habit  or  condition. 

Everytliing  which  can  be 
affirmed  must  come  under 
one  or  other  of  these  highest 
predicates,  wliich  were  de- 
scribed in  the  first  treatise  of 
Aristotle's  Oiganon,  called 
the  Categories. 

Cause,  meaning  of,  213. 

Aristotle  distinguished  foul 
kinds  of  causes  for  the  exist 
ence  of  a  thing — 1.  The  Ma 


INDEX  AND  QLOSSABY. 


817 


terial  Cause,  the  substance  or 
matter  composing  it ;  2.  The 
Formal  Cause,  the  pattern, 
type  or  design,  according  to 
which  il  is  shaped ;  3.  The 
Efficient  Cause,  the  force  em- 
ployed in  shaping  it ;  4.  The 
Final  Cause,  the  end,  motive 
or  purpose  of  the  work. 

Chance,  ignorance  of  the  causes 
which  are  in  action ;  see 
Probability. 

Character,  derivation  of  the 
word,  48. 

Circulus  in  definiendo,  239. 

Circulus  in  probando,  173. 

Clearness  of  knowledge,  57. 

Cognition,  {cognosco,  to  know,) 
knowledge,  or  the  action  of 
mind  in  acquiring  knowledge. 

Colligation  of  Facts,  Dr.  Whe- 
well's  expression  for  the  men- 
tal union  of  facts  by  some 
suitable  conception. 

Collective  terms,  21. 

Combined  or  complete  method 
of  investigation,  249. 

Comparison,  {com,  together ; 
par,  equal  or  like,)  the  action 
of  mind  by  which  we  judge 
whether  two  objects  of 
thought  are  the  same  or 
different  in  certain  points. 
See  Judgment. 

Compatible  terms  are  those 
which,  though  distiuct,  are 
not  contradictory,  and  can 
therefore  be  affirmed  of  the 


same  subject ;  as  "large  "  and 
"  heavy  ;"  "  bright-colored  " 
and  "  nauseous." 

Complex  conception,  infer 
ence  by,  92. 

Complex  sentence,  98 ;  syllo- 
gism, 141. 

Composition  of  Causes,  the 
principle  which  is  exemplified 
in  all  cases  in  which  the  joint 
effect  of  several  causes  is 
identical  with  the  sum  of  tlieir 
separate  effects.     J.  8.  Mill. 

Composition,  fallacy  of,  165. 

Compound  sentence,  94,  95. 

Comprehension  of  terms,  see 
Intension. 

Concept,  that  which  is  con- 
ceived, the  result  of  the  act 
of  conception  ;  nearly  synony- 
mous with    general    notion, 
idea,  thought. 

Conception  {con,  together ; 
capio,  to  take).  An  ambigu- 
ous  term,  meaning  properly 
the  action  of  mind  in  which 
it  takes  several  things  to- 
gether, so  as  to  form  a  general 
notion  ;  or,  again,  in  which  it 
forms  "  a  mental  image  of  the 
several  attributes  given  in 
any  word  or  combination  of 
words."    Mansel. 

Conceptualists,  14. 

Concrete  terms,  22. 

Conditional  propositions,  149. 

Confusion  of  words,  ambiguity 
from,  33. 


318 


htdbx  and  olossaby. 


Conjugate  words,  those  which 
come  from  the  same  root  or 
stock,  as  known,  knowing, 
knowingly,  knowledge. 

Connotation  of  terms,  43 ; 
ought  to  be  exactly  fixed,  247. 

Consciousness,  the  immediate 
knowledge  which  the  mind 
has  of  its  sensations  and 
thoughts,  and,  in  general,  of 
all  its  present  operations. 
Beid. 

Consectary=Corollary. 

Consequence,  the  connection 
between  antecedent  and  con- 
sequent ;  but  often  used  am- 
biguously for  the  latter. 

Consequent  of  a  hypothetical 
proposition,  150. 

Consequent  or  effect  of  a  cause, 
214. 

Consequent,  fallacy  of  the,  175. 

Consilience  of  inductions,  the 
agreement  of  inductions  de- 
rived from  different  and  inde- 
pendent series  of  facts,  as 
when  we  learn  the  motion  of 
the  earth  by  entirely  different 
modes  of  observation  and 
reasoning.      Whewdl. 

Consistency  of  propositions, 
83. 

Consistent  terms,  see  compat- 
ible terms. 

Contingent,  (contingo,  to  touch,) 
that  which  may  or  may  not 
happen  ;  opposed  to  the  necea- 
viry  and  impossible. 


Contingent  matter,  85. 

Continuity,  Law  of,  the  prin- 
ciple that  nothing  can  pass 
from  one  extreme  to  another 
without  passing  through  all 
the  intermediate  degrees ; 
motion,  for  instance,  cannot 
be  instantaneously  produced 
or  destroyed. 

Contradiction,  Law  of,  105. 

Contradictory  terms.  26 :  prop- 
ositions, 83. 

Contraposition,  conversion  by, 
89. 

Converse  fallacy  of  accident, 
169. 

Conversion  of  propositions, 
86 ;  with  quantified  predicate. 
266. 

Convertend,  87. 

Co-ordinate  propositions,  96. 

Copula,  65. 

Corollary,  a  proposition  which 
follows  immediately  from  an- 
other which  has  been  proved. 

Correlative  terms,  27. 

Criterion  {KpLrijptnv,  from  Kplvut, 
to  judge),  any  fact,  rule, 
knowledge,  or  means  requi- 
site to  the  formation  of  a 
judgment  which  shall  decide 
a  doubtful  question. 

Cross  division,  235. 

Data,  (plural  of  datum,  that 
which  is  given,)  the  facts  or 
assertions  from  which  an  in- 
ference is  to  be  drawn. 


rSDEX  AND  GLOSSABT. 


819 


Deduction  and  Induction,  178. 

Deductive  method,  227. 

De  facto,  what  actually  or 
really  happens;  opposed  to 
dejure,  what  ought  to  happen 
by  law  or  right. 

Definition,  the  logical  process, 
238 ;  of  logic,  1. 

Degree,  terms  expressing,  26 ; 
questions  of,  107. 

Demonstration,  {demonstro,  to 
point  out,)  strictly  the  point- 
ing out  the  connection  be- 
tween premises  and  conclu- 
sion. The  term  is  more 
generally  used  for  any  argu- 
ment or  reasoning  regarded 
as  proving  an  asserted  con- 
clusion. A  demonstration  is 
either  Direct  or  Indirect.  In 
the  latter  case  we  prove  the 
conclusion  by  disproving  its 
contradictory,  or  showing 
that  the  conclusion  cannot  be 
supposed  untrue. 

Demonstrative  Induction,  182. 

Descartes,  Rene,  a  French 
philosopher  and  mathema- 
tician of  the  most  distin- 
guished originality  (1596- 
1650) ;  author  of  La  Dis- 
cours  de  la  Method,  Les  Prin- 
eipes,  Les  Meditations,  and 
other  works.  Descartes  has 
been  called  "the  Father  of 
Modem  Psychology. "  His 
criterion  of  truth  was  the 
tleamess  of  ideas.    His  first 


principle  of  knowledge,  which 
he  declared  was  left  certain 
when  everything  else  was 
denied,  is  expressed  in  his 
now  famous  maxim :  Cogito, 
ergo  sum.  Descartes'  method 
was  largely  suggested  by 
mathematical  method.  He 
believed  that  the  mind  ought 
to  be  studied  by  the  examina- 
tion of  consciousness,  or  by 
what  has  now  come  to  be 
known  as  the  introspective 
method. 

Descartes  on  Method,  261. 

De  Morgan's  logical  discov 
eries  and  writings,  271. 

Denotation  of  terms,  41. 

Depth  of  a  notion,  see  Inten- 
sion. 

Derivatives  from  the  root  spec, 
sight,  55. 

Description,  see  Accidental 
Defin  ition. 

Destructive  dilemma,  159. 

Desynonymization  of  terms, 
51. 

Determination,  the  distin- 
guishing of  parts  of  a  genua 
by  reunion  of  the  genus  and 
difference.     See  Division. 

Development  of  a  term,  274 

Diagrams,  of  sentences.  99, 
103 ;  of  syllogisms,  120, 121  ; 
of  propositions,  88. 

Dialectic  (JtaP^e^rtx^  TeKV7i„  the 
art  of  discourse,  from  Stalk' 
yeadai,    to    discourse),     Tb« 


820 


DTDEX  AKD  GLOSSABT, 


original  name  of  Logic,  per- 
haps invented  by  Plato ;  also 
liBod  to  denote  the  Logic  of 
Probable  Matter  (Aristotle), 
the  right  use  of  Reason  and 
Language,  the  Science  of  Be- 
ing ;  it  is  thus  a  highly  am- 
biguous term. 

Dichotomy,  division  by,  107, 
286. 

Dicta,  de  omni  et  nuUo,  111, 

Difference,  the  predicable,  228. 

Differentiation  of  terms,  51. 

Dilemma,  158. 

Disbelief,  the  state  of  mind  in 
which  we  are  fully  persuaded 
that  some  opinion  is  not  true. 
J.  8.  Mill.  It  is  equivalent 
to  belief  in  the  contradictory 
opinion  or  assertion,  and  is 
not  to  be  confused  with 
Doubt,  which  see. 

Discourse,  or  reasoning,  16. 

Discovery,  method  of,  199. 

Disjunctive,  propositions,  150; 
syllogism,  156. 

Distinct  knowledge,  55. 

Distribution  of  terms,  79. 

Division,  logical,  234;  meta- 
physical, 288 ;  fallacy  of, 
166. 

Doubt,  {dubito,  to  go  two 
ways,)  the  state  of  mind  in 
which  we  hesitate  between 
two  or  more  inconsistent 
opinions.     See  Difbdief. 

Drift  of  a  proposition,  the  vary- 
ing meaning  which  may  be 


attributed  to  the  same  sen 
tence  according  to  accentua 
tion.  See  FaUacy  of  accent, 
167. 

Empiricism  {ifineifyia,  experi- 
ence), the  doctrine  of  those 
who  consider  that  all  knowl- 
edge  is  derived  merely  from 
experience. 

Empirical  Law,  249. 

Enthymeme,  142. 

Epicheirema,  145.  , 

Episyllogism,  144. 

Equivocal  terms,  81. 

Equivocation,  causes  of,  88 , 
fallacy  of,  163. 

Essence,  {essentia,  from  esse,  to 
be,)  "  the  very  being  of  any. 
thing,  whereby  it  is  what  it 
is."  Locke.  It  is  an  ancient 
scholastic  word,  which  cannot 
be  really  defined,  and  should 
be  banished  from  use. 

Essential  propositions,  72. 

Euler's  diagrams,  120,  121. 

Evidence,  (e,  and  videre,  to 
see,)  literally  the  seeing  of 
anything.  The  word  now 
means  any  facts  apprehended 
by  the  mind  and  made  the 
grounds  of  knowledge  and 
belief. 

Examples,  use  of,  175. 

Exceptive  propositions,  72. 

Excluded    middle,     law     of 
166. 

Exclusive  propositions,  72. 

Exhaustive  division,  107, 236 


HTDEX  AND  GLOSSARY. 


831 


Ezperimentum  cnicis,  an  ex- 
periment which  decides  be- 
tween two  rival  theories,  and 
shows  wliich  is  to  l)e  adopted, 
as  a  finger-post  shows  which 
of  two  roads  is  to  be  taken. 

Explanation,  of  facts,  255 ;  of 
laws,  256. 

Explicative  propositions,  72. 

Exposita,  a  proposition  given 
to  be  treated  by  some  logical 
process. 

Extension  and  intension,  39. 

Extensive  Syllogism,  149. 

Extremes  of  a  proposition,  are 
its  ends  or  terms,  the  subject 
and  predicate. 

Fact,  212. 

Fallacy,  purely  logical,  163; 
semi-logical,  162;  material, 
169 ;  in  hypothetical  syllo- 
gism, 155 ;  in  dilemma,  158. 

False  cause,  fallacy  of,  175. 

False  propositions,  74. 

Figure  of  speech,  fallacy  of, 
168. 

Figures  of  the  syllogism,  127  ; 
their  uses,  130. 

Form  and  matter  of  thought, 
5. 

Fundamentum  divisionis,  234. 

Fundamentum  relationis,  the 
ground  of  relation,  i.e.,  the 
series  of  events  or  circum- 
stances which  establish  a  re- 
lation between  two  correlative 
terms. 


Fundamental  principles  of  sy) 
logism,  108. 

Galenian,  or  fourth  figure  o 

the  syllogism,  131. 
General    notions,    14;    temu^ 

20. 
Generalization  of  names,  47. 
Generic  property,  232. 
Genus,    228 ;   generalissimum, 

230. 
Geometiical     reasoning,     61, 

187 ;  Pascal  on,  258. 
Grammatical     predicate,    98  i 

sentence.  68. 
Gravitation,  theory  of,  252. 

Hamilton,  Sir  William,  a 
Scotch  philosopher  (1788- 
1856);  professor  at  the  Uni 
versity  of  Edinburgh  (1836- 
1856) ;  author  of  Discussions 
in  Philosophy  and  Literature, 
largely  reprinted  from  his 
essays  in  the  Edinburgh  Re- 
tiew,  Lectw-es  on  Metaphysics, 
&aA  Lectures  on  Logic.  Hamil- 
ton wae  the  most  erudite 
philosopher  of  his  time  in 
Great  Britain. 

Hamilton,    Sir  W.,  Method  of 
Notation.  268. 

Heterogeneous,  230 ;  intermix- 
ture of  effects,  224. 

Homogeneous,  268 ;  intermix 
ture  of  effects,  224. 

Homologue,'whatever  is  homci 
ogoua. 


322 


INDEX   AND  GLOSSABT. 


Homologfy,  a  special  term  for 
the  analogy  existing  between 
parts  of  different  plants  and 
animals,  as  between  the  wing 
of  a  bird  and  the  lore  leg  of  a 
quadruped,  or  between  the 
scales  of  a  fish  and  the 
feathers  of  a  bird. 

Homonymous  terms,  32. 

Hypothesis,  208. 

Hypothetical  propositions,  66 ; 
syllogism,  15. 

Idea  (l()ia,  tldoc,  image),  a  term 
used  ambiguously,  but  gener- 
ally equivalent  to  thought, 
notion,  concept.  Defined  by 
Locke  as  "  Phantasm,  notion, 
species,  or  whatever  it  is 
which  tlie  mind  can  be  em- 
ployed about  in  thinking." 
To  have  an  idea  of  a  thing  is 
to  think  of  that  thing. 

Identity,  law  of,  104. 

Idol  (n^(j?.oi;  fMof,  image). 
Bacon's  figurative  name  for 
the  sources  of  error ;  he  enu- 
merated four  kinds  ,  Idols  of 
the  Tribe,  whicii  affect  all 
people;  Idols  of  the  Cave, 
which  are  peculiar  to  an  in- 
dividual ;  of  the  Forum, 
which  arisi"  in  the  intercourse 
of  men;  of  the  Theatre, 
which  proc»'ed  from  the  sys 
terns  of  phihisophers. 

Ignoratio  Elenchi,  172. 

Illation  (/^a^uni,  past  participle 


of  infero,  to  bring  in).  S« 
Inference. 

Illative,  that  which  can  be  in- 
ferred. 

Illicit  process,  of  the  minoi 
term,  119 ;  of  the  major  term, 
128. 

Immediate  inference,  86. 

Imperfect  figures  of  the  syllo- 
gism, 145. 

Imperfect  Induction,  181. 

Impossible  matter,  85. 

Inconsistent  terms  imply  qual- 
ities which  cannot  coexist  in 
the  same  thing.  See  compat- 
ible terms. 

Inconsistent  propositions,  83. 

Indefinite  proi)Ositions,  68. 

Indefinite  or  infinite  term,  is 
a  negative  term  whicli  only 
marks  un  object  by  exclusion 
from  a  class. 

Indesignate  propositions.  See 
Indefinite  propositions. 

Indirect  demonstration.  See 
Demonstration. 

Indirect  inference,  method  of, 
138. 

Indirect  reduction  of  the  syl- 
logism, 137. 

Individual,  what  cannot  be 
divided  witiiout  losing  ita 
name  and  distinctive  qiiali- 
tips,  although  generally  capa- 
ble of  physical  division  oi 
partition,  which  see. 

Induction,  178. 

Inductive  syllogism,  183,  184. 


INDEX  ASD  GLOSS ABT. 


Inference,  defined,  86;  imme- 
diate, 87;  mediate,  113. 

Infima  species,  230. 

Innate  ideas,  see  a  priori 
truths. 

Inseparable  accident,  232. 

Intension  and  extension  of 
terms.  39 ;  law  of  relation, 
42. 

Intensive  syllogism,  149. 

Intention,  first  and  second,  a 
distinction  between  terms 
thus  defined  by  Hobbes ;  "  Of 
the  first  intention  are  the 
names  of  things,  a  man, 
stone,  &c. ;  of  the  second 
are  the  names  of  names,  and 
speeches,  as  vniversal,  par- 
ticular, genus,  species,  syllo 
ffism,  and  the  like."  A  term 
of  the  second  intention  ex- 
presses the  mode  in  which 
the  mind  regards  or  classi- 
fies those  of  the  first  inten- 
tion. 

Intermediate  link,  explanation 
by,  256. 

Intuitive  knowledge,  57. 

Irrelevant  conclusion,  fallacy 
of,  171. 

Judgment,  13. 

Language,  the  subject  of  logic, 

10. 
Language,  three  purposes  of, 

245. 
Laws  of  thought,  2,  104 


Leibnitz  (1646-1716),  the  great 
est  of  the  earlier  German 
philosophers  and  celebrate<f 
as  a  matliematician  and  uni 
versal  genius ;  author  ol 
Nouveaux  Essais  sitr  I'  Etu 
tendement  Hu-nain,  and  La 
Theodicee  Leibnitz  invented 
the  infinitesimal  calculus  at 
the  same  time  as  Newton. 
Although  he  advocated  some 
strange  doctrines,  Leibnitz 
must  be  regarded  as  one  of 
the  greatest  intellects  which 
the  world  has  known.  He 
criticised  the  foundations  of 
human  knowledge  as  they 
were  set  forth  by  Locke,  and 
maintained  that  there  is  an. 
other  source  of  knowledge 
than  experience,  the  intui- 
tions of  the  mind. 

Leibnitz  on  knowledge,  56. 

Lemma  Qiafijidvu,  to  take  or 
assume),  a  proposition,  a  pre- 
mise granted ;  in  geometry, 
a  preliminary  proposition. 

Limitation,  conversion  by,  87. 

Locke,  John,  an  English  phy- 
sician and  philosopher  (1632- 
1704);  influential  also  as  a 
writer  on  government  and 
religious  toleration  ;  author  of 
the  celebrated  work  Essay 
Concerning  Human  Under' 
stnndi/if/,  an  epoch-making 
production  in  which  human 
knowledge  is  referred  entirely 


324 


INDEX   AND   GLOSSARY. 


to  experience,  to'  the  exclu- 
sion of  any  innate  element. 
Locke  may  justly  be  regarded 
as  the  founder  of  the  Eng- 
lish school  of  psychology. 
His  influence  in  France  was 
also  great.  In  Germany 
Locke  was  less  followed  and 
has  been  severely  reviewed 
by  Leibnitz  and  otiiers.  It  is 
likely  that  he  did  not  see  all 
the  ultimate  bearings  of  his 
doctrines.  He  advocated  the 
doctrine  of  representative 
ideas,  which  prepared  the 
way  for  the  doctrines  of 
Hume  and  of  Berkeley,  and 
has  been  ably  reviewed  by 
Thomas  Reid  and  Sir  W. 
Hamilton. 

Logic,  derivation  of  name,  1, 

Logical  abacus,  slate  and  ma- 
chine. 280. 

Logomachy,  a  war  of  words. 

Lowest  species,  230. 

Machine,  the  logical,  280. 

Major,  term,  116;  premise, 
116. 

Many  questions,  fallacy  of, 
176 

Material  fallacies,  169. 

Mathematical  induction,  187. 

Matter  of  thought,  6;  of  pro- 
positions, 85. 

Matter  is  defined  by  J.  S.  Mill 
as  "  the  external  cause  to 
which  we  ascribe  our  sensa- 


tions," or  as  Permanent  Pos- 
sibility of  Sensation, 

Mediate  inference,  113. 

Membra  dividentia,  the  parts 
into  which  a  class  is  divided  ; 
the  constituent  species  of  a 
genus. 

Metaphor,  52. 

Metaphysical  division,  238. 

Metaphysics  (ru  fieru  ru  ^vai- 
Ku),  the  works  of  Aristotle 
which  followed  or  were 
studied  after  his  Physics. 
First  Philosophy,  or  the  so- 
called  science  of  things  in 
their  own  nature;  ontology 
or  the  science  of  Being. 

Method  {(liOoioc,  nera  and  6()6(, 
way),  mode,  way  or  instru- 
ment of  accomplishing  an 
end. 

Method,  201 ;  Pascal  on,  257 ; 
Descartes*  Discourse  on,  263. 

Methods  of  Induction,  Agree- 
ment, 215  ;  Diflference,  216  ; 
of  Experiment,  218;  Joint 
Method,  219;  Residues,  224; 
Ck)ncomitant  Variations,  221. 

Metonymy  (nerd,  and  6vo/ia, 
name),  grammatical  name  for 
the  transfer  of  meaning  of  a 
word  to  a  closely  connected 
thing,  as  when  we  speak  of 
the  church,  meaning  the 
people  in  it.  See  Transfer 
of  meaning. 

Middle  Term,  114. 

Mill,  John  Stuart,  an   English 


INDEX  AND  GLOSSARY. 


335 


philosopher  and  economist 
(1806-1873);  son  of  James 
Mill,  whose  doctrines  with 
some  modifications  he  taught; 
author  of  A  System  of  Logic, 
(in  which  the  syllogism  is 
severely  criticised  and  much 
is  made  of  induction,)  numer- 
ous political  and  sociological 
works,  and  An  Examination 
of  the  Philosophy  of  Sir  W. 
Hamilton.  Mill  was  an  em- 
piricist in  philosophy  and  a 
utilitarian  in  morals.  His 
writings  have  been  severely 
criticised  by  Professor  Jevons 
in  a  series  of  articles  in  the 
Contemporary  and  other  re- 
views. 

Mill,  J.  S.,  on  Connotative 
terms,  43 ;  on  Induction,  183, 
215  ;  on  Observation,  206. 

Minor  term,  116  ;  premise,  118. 

Mnemonic  verses,  Barbara, 
etc.,  133. 

Modal  propositJon,  73. 

Modus,  ponens,  151 ,-  toUens, 
151. 

Modus,  ponendo  toUem,  156 ; 
tollendo  ponens,  157. 

Moods  of  the  syllogism,  134; 
according  to  Hamilton,  268. 

Muller,  F.  Max,  a  German 
philologist  of  note  (born  in 
1823),  still  (1883)  and  for  a 
long  time  a  resident  in  Eng- 
land and  professor  at  Ox- 
ford   University.      Professor 


Muller  is  a  fascinating  and 
informing  writer,  but  his 
theories  of  language  have 
been  severely  criticised  by 
Professor  W.  D.  Whitney, 
an  American  philologist  and 
professor  in  Yale  College. 

Name,  or  term,  17. 

Necessary  matter,  85. 

Necessity  {ne,  not;  and  cesso, 
to  cease),  that  which  always 
is  and  cannot  but  be. 

Negation,  conversion  by,  88. 

Negative,  terms,  24;  proposi- 
tions, 24;  premises,  fallacy 
of,  102. 

Newton's  experiments,  253. 

Nominal  definitions,  359. 

Nominalists,  14. 

Non  causa,  pro  causa,  175. 

Non  sequitur,  175. 

Notion  {nosco,  to  know),  the 
action  of  apprehending  or 
taking  note  of  the  various 
qualities  of  an  object ;  or 
more  commonly  the  result  of 
that  action.  See  Idea,  Con- 
cept. 

Notiora  naturae,  199. 

Novum  Organum,  first  apho- 
risms of,  202. 

Numerically  definite  syllogism, 
184. 

Object  of  verb,  98. 
Objective,  that  which  belongs 
to  the  object  of  thought,  the 


326 


INDEX   AND  GLOSSARY, 


non-ego;  opposed  to  Sub- 
jective, which  see. 

Obscure  knowledge,  57. 

Observation,  20G. 

Occasion  of  an  event,  the  proxi- 
mate cause,  or  last  condition 
which  is  requisite  to  bring 
other  causes  into  action,  213. 

Opposite  terms,  24. 

Opposition  of  jiropositions,  83. 

Organon  (Jipyavov,  Latin  Or- 
ganum.  Instrument),  a  name 
for  Aristotle's  logical  trea- 
tises, first  generally  used  in 
the  15th  century,  implying 
that  they  may  be  regarded  as 
an  instrument  to  assist  the 
mind.  The  name  was  adopted 
by  Bacon  for  his  Novum  Or- 
ganum. 

Paradox  (jrapu,  66^a,  contrary  to 
opinion),  an  assertion  con- 
trary to  common  opinion,  and 
which  mav  or  may  not  prove 
true  ;  often  wrongly  used  to 
mean  what  is  self-contradic- 
tory and  absurd. 

Paralogism  (Kapa?.oyi^o/iat,  to 
reason  wrongly),  a  purely 
logical  fallacy,  or  breach  of 
the  rules  of  deductive  logic. 

Parity  of  reasoning,  an  expres- 
sion used  to  denote  that  when 
one  case  has  been  demon- 
strated, other  similar  cases 
can  be  demonstrated  by  a  like 
course  of  reasoning. 


Paronymous  words,  see  Congu- 
gate  words. 

Particular  propositions,  67. 

Particular  premises,  fallacy 
of,  162. 

Partition  or  physical  divi- 
sion, 238. 

Pascal,  Blaise,  a  French  thinker 
of  wonderful  genius  and  not 
less  distinguished  piety  (1623- 
1662),  who  excelled  in  geom- 
etry and  other  branches  of 
mathematics  ;  author  of  the 
famous  Provincial  Letters,  in 
which  he  powerfully  de- 
nounces the  Jesuits,  and  the 
still  more  celebrated  Thoughts, 
designed  to  humble  the  rea- 
son of  man  in  the  presence 
of  the  great  mysteries  of  be- 
ing and  lead  to  a  devout 
Christian  faith.  His  works 
are  characterized  by  remark- 
able insight,  dialectic  skill 
and  eloquence. 

Per  accidens,  conversion,  87. 

Perfect  Figure  of  the  Syllo- 
gism,  134. 

Perfect  knowledge,  characters 
of,  56. 

Periodic  changes,  228. 

Peripatetic  Philosophy  (nepi- 
naTEu,  to  walk  about),  the 
name  usually  given  to  the 
doctrines  of  Aristotle  and  his 
followers,  who  are  said  to 
have  carried  on  their  studies 
and  discussions  while  walking 


rNDBX  AND   GLOSSABT. 


837 


about  the  halls  and  prome- 
nades of  the  Lyceum. 

Petitio  Principii,  173. 

Phenomenon,  213. 

Physical  definition  assigns  the 
parts  into  which  a  tiling  may 
be  separated  by  partition  or 
physical  division. 

Polylemma,  an  argument  of 
the  same  form  as  a  dilemma, 
but  in  which  there  are  more 
than  two  alternatives. 

Porphyry,  tree  of,  233. 

Port  Royal  Logic,  359. 

Positive  terras,  34. 

Post  hoc,  ergo  propter  hoc, 
175. 

Postulate  ( postulatum,  a  thing 
demanded),  a  proposition 
which  is  necessarily  demanded 
as  a  basis  of  argument ;  in 
geometry,  the  postulates  de- 
fine the  practical  conditions 
required. 

Predicables,  237. 

Predicaments  ( prcedicamenta, 
what  can  be  predicated),  see 
Categories. 

Predicate,  66,  80,  98,  363. 

Premise,  or  Premiss,  113. 

Primary  Laws  of  Thought,  104, 

Principle  {principium,  begin- 
ning), the  first  source  of  any- 
thing ;  sometimes  specially 
used  to  mean  the  major 
premise  of  a  syllogism. 

Privative  conception,  infer- 
ence by,  91. 


Privative  terms,  26. 

Probability,  quantity  or  de 
gree  of  belief,  or  more  truly 
quantity  of  information  con- 
cerning an  uncertain  event, 
measured  by  the  ratio  of  the 
number  of  cases  favorable  to 
the  event  to  the  total  number 
of  cases  which  are  ])ossil)ie. 

Probability,  of  propositions, 
74 ;  of  inductions,  181. 

Problem  (Trpo/i/.^y/zajthat  which. 
is  thrown  down),  an  assertion 
put  forward  for  proof  or  dis 
proof. 

Proof,  the  assigning  a  reason 
or  argument  for  the  support 
of  a  given  proposition. 

Proper  names,  29,  32,  44. 

Propositions,  see  the  c?iap. 
ter  on,  pp.  64,  99,  and  the 
particular  references  in  this 
Index. 

Prosyllog^sm,  144. 

Proximate  genns,  337. 

Quantification    of     predicate, 

363 
Quantity  of   propositions,  67; 

questions  of  quantity,  68. 
Quaternio  terminorum,  162. 

Ramean  tree,  see  Tree  of  Por- 
phyry. 

Ratiocination,  a  name  equiva- 
let  to  Syllogism  or  Deduo 
tion,  adopted  by  J.  S.  MilL 

Realism,  14. 


328 


INDEX   AND   GLOSSARY. 


Reason  {ratio  from  re^r,  to 
think),  a  term  of  wide  and 
ambiguous  meaning?;  it  has 
sometimes  been  special  \y  used 
to  denote  the  minor  premise 
of  a  syllogism. 

Reasoning,  or  discourse,  15. 

Record,  language  as  instru- 
ment of,  245. 

Reductio  ad  absurdum  or  ad 
impombile,  an  indirect  dem- 
onstration founded  upon  the 
impossibility  of  a  contradic- 
tory supiwsition. 

Reduction  of  the  syllogistic 
figures,  135  ;  of  hypothetical 
to  categorical  syllogisms,  153. 

Relation  {relatum,  past  parti- 
ciple of  refero,  to  bear  back), 
any  connection  in  thought  or 
fact  between  two  things. 

Relative  terms,  27. 

Residual  phenomena.  226. 

Residues,  method  of,  225. 

Rules  of  the  syllogism,  113. 

Scholastic  Philosophy,  a  gen- 
eral name  for  the  systems  of 
philosophy  taught  during  the 
middle  ages  from  the  9th  to 
the  16th  century,  flourishing 
chiefly  in  the  13th  and  14th 
centuries.  The  subject  was 
chiefly  the  logic  of  Aristotle, 
varied  with  theology,  meta- 
physics, grammar,  or  rhetoric. 

Second  Intention,  see  Inten- 
tion. 


Secundi  adjaamt's,  of  the 
second  adjacent,  an  expres- 
sion in  incorrect  Latin,  ap 
plied  to  a  grammatical  sen- 
tence or  proposition  contain- 
ing only  two  parts,  the  8ul> 
ject  and  verb,  without  a  dis- 
tinct copula. 

Self-contradictory  terms,  26. 

Semilogical  fallacies,  162. 

Sentence,  grammatical,  65. 

Separable  accident,  232. 

Significates  of  a  term  are 
things  denoted  or  signified  by 
it. 

Similars,  substitution  of,  282. 

Simple,  apprehension,  12  ;  con- 
version, 88.  266. 

Singular,  terms,  20;  proposi- 
tions, 69. 

Sophism  ((joijuafia,  from  ao<^ia, 
wisdom),  a  false  argument ; 
the  name  often  implies  that  a 
false  argument  is  consciously 
used  for  deception. 

Sorites,  145. 

Specialization  of  names,  60. 

Species,  in  logic,  228;  in 
natural  history,  231. 

Spencer,  Herbert,  a  contempo- 
rary English  thinker  and 
writer  of  great  ability  and 
influence  (1820);  author  of 
many  miscellaneous  works, 
but  most  celebrated  as  the 
writer  of  the  Synthetic  Phil 
osophy,  an  undertaking  of 
great    magnitude    not     yet 


INDEX   AND   GLOSSARY. 


329 


(1888)  completed.  Spencer 
has  covered  nearly  the  whole 
range  of  speculative  thought, 
and  his  aim  is  to  apply  the 
doctrine  of  evolution  to  every 
department  of  knowledge. 
He  is  a  clear  and  instructive, 
but  sometimes  a  misleading, 
writer,  as  any  one  is  likely  to 
be  who  undertakes  to  culti- 
vate so  wide  a  field  in  the 
service  of  a  theory  already 
formed  rather  than  derived 
from  a  minute  study  of  the 
facts  in  the  different  depart- 
ments of  knowledge. 

Subaltern,  propositions,  82 ; 
genera  and  species,  233. 

Subalternans,  subalternates, 
83. 

Subcontrary  Propositions,  83. 

Subject  of  a  proposition,  66. 

Subjective,  that  which  belongs 
to  the  thinking  subject,  the 
ego,  or  mind  engaged  in 
thought ;  opposed  to  objective, 
which  see. 

Subordinate  propositions,  97. 

Substance  (sub,  under ;  stans 
from  stare,  to  stand),  that 
which  underlies  and  bears 
phenomena  •  or  attributes  ; 
strictly  speaking  it  is  either 
mind  or  matter,  but  it  is 
more  commonly  used  in  the 
material  sense. 

Substitution  of  similars,  see 
timHtvrt. 


Subsumption  {sub,  under;  aumo, 
to  take  or  put),  a  name  used 
by  Sir  W.  Hamilton  for  the 
minor  premise  of  a  syllo- 
gism, because  it  brings  or 
subsumes  a  special  case  under 
the  rule  expressed  in  vhe 
major  premise  or  sumption. 

Subsumption  of  a  law  is  Mr. 
Mill's  expression  for  the  third 
mode  of  explaining  a  law  by 
showing  it  to  be  a  particu- 
lar case  of  a  more  general 
law 

Sufficient  Reason,  Principle  or 
Law  of,  113. 

Sui  generis,  230. 

Summum  genus,  230. 

Sumption  {sumo,  to  take),  Sir 
W.  Hamilton's  name  for  the 
major  premise  of  a  syllo- 
gism. 

Syllogism,  10,  113;  inductive, 
178. 

Symbolical  knowledge,  60. 

Syncategorematic  words,  18. 

Synthesis,  200. 

Synthetic  syllogism,  a  syllo- 
gism in  which  the  conclu- 
sion stands  last ;  see  Analytie 
syllogism. 

System,  {avarrjfiu,  from  awicr' 
TTjui,  to  put  together),  a  con. 
nected  body  of  knowledge. 

Tacit  premise,  143. 
Tautologous  propositions,  73. 
Tendency,  313. 


330 


INDEX   AND  GLOSSARY. 


Terms,  see  chapter  an,  pp.  17, 
62. 

Tertii  adjacentis,  of  the  third 
adjacent,  an  expression  in  in- 
Borrect  Latin,  applied  to  a 
grammatical  sentence  or  prop- 
osition in  which  the  subject, 
copula  and  predicate,  are  all 
distinctly  stated. 

Theory  {ffFupiu,  contemplation), 
knowledge  of  principles,  as 
opposed  to  practice  ;  ambigu- 
ously used, see  p.  210. 

Thesis  (fitao.,  from  t'lBtjui,  to 
place),  an  assertion  or  propo- 
sition which  is  put  forth  to  be 
proved  or  supported  by  argu 
ments. 

Thoughts  or  things,  the  object 
of  logic,  11. 

Totum  divisum,  a  class  or 
notion  which  is  divided  into 
parts  by  a  difference. 

Traduction,  179. 

Transfer  of  meaning  of  terms, 
35. 

Tree  of  Porphyry,  232. 

Trilemma,  an  argument  resem- 
bling a  dilemma,  but  in  which 
there  are  three  alternatives. 

Truth,  conformity  of  our 
knowledge  with  the  things 
known. 


Ultra-total  distribution,  266. 
Uniformity  of  nature,  185. 
Universal     propositions,    6? 

70 ;  affirmative,  68 ;  negative 

67. 
Univocal  terms,  31. 

Variations,  method  of,  221. 
Verb,  94 

Watts,  Isaac,  an  English 
clergyman,  hymn-writer  and 
theologian  (1674-1748) ;  authoi 
of  a  useful  practical  work  on 
logic  which  was  very  populai 
in  its  lime,  but  which  is  nowi 
little  known. 

Weakened  conclusion,  129. 

Whately,  Richard,  Archbishop 
of  Dublin,  an  English  eccle- 
siastic and  writer  on  logic, 
political  economy  and  rhetoric 
(1787-18(53);  r.  shrewd  and 
ingenious  writer,  but  lacking 
in  profound  erudition  as  a 
logician.  Whately's  works 
on  logic  and  rhetoric  have 
been  until  recently  very  pop- 
ular, especially  in  America 
as  text-books  on  these  sub. 

jects. 
Worse     relation    (Hamilton) 

370. 


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